Preliminary note: This article contemplates seasonal staff who are compensated primarily or entirely with free tuition. For your year-round, salaried staff who have kids in camp, free camp is likely considered a fringe benefit and should be treated like other fringe benefits. See here for an IRS overview.
In our industry, it's common for parents to work at camp in exchange for free tuition for their campers. While we often colloquially refer to these as "volunteer" arrangements, they're typically considered "barter/in-kind compensation" under the law—and there's an important distinction between the terms.
A volunteer donates their time to support a nonprofit organization in exchange for no compensation, except for reimbursement of the volunteer's expenses. By contrast, in a barter/in-kind compensation arrangement, the camp parent is indeed compensated, albeit with camp tuition rather than a paycheck.
A Conversation for Your Accountant
Volunteer work doesn't entail taxable income, but barter work does. As the IRS explains in Publication 525, "Bartering is an exchange of property or services. You must include in your income, at the time received, the [fair market value] of property or services you receive in bartering."
The IRS gives the following example of two independent contractors:
You're a self-employed accountant. . . . In return for accounting services you provided, [a] house painter painted your home. You must report as your income on Schedule C (Form 1040) the [fair market value] of the house painting services you received. The house painter must include in income the [fair market value] of the accounting services you provided.
Thus, as a Wolters Kluwer article explains, "Exchanging goods and services with another business owner—bartering—is a common practice, and can make excellent sense in today's economy, but the IRS is warning that 'barter dollars' are equal to 'real dollars' for tax purposes."
This is something to discuss with your accountant. Following a detailed review of your specific circumstances, your accountant should advise you about the proper tax reporting of barter arrangements.
Keep in mind, the barter example above envisions a relationship between 1099 independent contractors, not between a business and W-2 employee. In the employment relationship, among other questions, you should ask your accountant and/or payroll provider about how to issue a W-2 and pay taxes for in-kind wages.
Employee or Independent Contractor?
Let's briefly consider the distinction between an employee and independent contractor, which is an important one for barter arrangements.
While a particular person's status as an employee or independent contractor depends on the totality of their relationship with the employer, the Department of Labor provides a useful summary and comparison of some characteristics that are relevant to the analysis:

Bartering with Independent Contractors
Conceptually, working with an independent contractor is more like hiring an outside business to provide a service, and less like hiring a counselor whose work you control and direct all summer.
The classic example of an independent contractor is an electrician who comes to your camp to install a couple outlets and then heads to the business down the road to fix their lights. This is obviously a different kind of relationship than the one you have with counselors, who are your employees.
Of course, there's a spectrum of personnel between the classic independent contractor and the classic employee. Taking into account the factors above and other applicable laws and guidance, it's entirely possibly that some of the parents with whom your camp barters are in fact independent contractors.
The distinction is important because, unlike employees, independent contractors aren't subject to the federal and state employment laws. This means you're free to negotiate the terms of payment with an independent contractor without being bound by minimum wage and overtime considerations. Of course, this assumes that the independent contractor is properly classified as such and is not a misclassified employee.
When you barter with a true independent contractor, the arrangement is fairly straightforward: the independent contractor provides a service, the camp provides free tuition in exchange for that service, and the minimum wage and overtime laws are not implicated. As noted above, your accountant can advise you on how this arrangement should be taxed.
Bartering with Employees
Now let's assume you'd like to barter with an employee rather than an independent contractor. Here things become a bit more complicated because employees are subject to minimum wage and overtime laws, unless they're exempt. Camps typically rely on the "seasonal amusement/recreation exemption" and its state analogs, but those exemptions don't apply to every camp.
Subject to certain conditions, Section 3(m) of the federal Fair Labor Standards Act allows employers to count "board, lodging, and other facilities" as wages. Using a specific example from the law, the term other facilities includes "tuition furnished by a college to its student employees"—which certainly seems analogous to a tuition waiver from camp.
If a camp is not exempt, then it's critical that its employees are paid minimum wage and overtime for all hours worked. And even if a camp is exempt, wage rate notification laws typically require that employees are clearly informed of how much they earn in exchange for their work.
This is Where Good Contracts Come In
Whether a particular employment relationship is exempt or not, and whether your camp is bartering with an independent contractor or another business, the best practice—and, often, the legal mandate—is to put the compensation details in writing.
Camps should have a contract for each barter/in-kind compensation arrangement to establish the value of the camp's tuition along with the details of the exchange. And in the case of camps that are not exempt from minimum wage and overtime obligations, their offer letter should ensure that employees are compensated at or above minimum wage while taking overtime obligations into account.
Important State Law Considerations
Many states require that employee wages are paid in "lawful money of the United States" and not by other means. Also, states often have specific rules and limitations regarding the payroll deductions that can be made for things like meals and lodging.
While these laws do not impact your relationship with independent contractors (discussed above) or volunteers (discussed below), state laws may significantly or entirely limit your ability to barter with employees. For each individual camp, this becomes an important state-specific question, which can only be side-stepped if you barter with a properly-classified independent contractor, provide an expense reimbursement to a properly-classified volunteer, or take the "Simpler Option" discussed in the following section.
A Simpler Option
If the prospect of extended calls with your accountant and attorney is giving you a headache, then you may consider a simple alternative: You can simply pay a staff parent for their work and then charge the parent for camp. In other words, you can pay a parent like you'd pay any other employee, and then you can charge the parent like you would charge any other family. Some camps may find this approach preferable because it fits neatly with their existing employment agreements and tax arrangements.
Nonprofit Camps: A Wrinkle Regarding Volunteers
As noted at the start of this article, volunteers typically provide charitable services to nonprofits for no compensation, except that they can be reimbursed for their expenses.
Note that there are a number of applicable legal requirements for a person to be properly classified as a volunteer. A camp parent who works for camp does not become a "volunteer" simply by virtue of getting free tuition. And if an employee is misclassified as a volunteer, then the camp can face not-insignificant legal and financial consequences.
If you do have a camp parent who's a properly-classified volunteer, then it's worth exploring whether you can provide free tuition as a reimbursement for the volunteer's expenses. This may avoid certain tax implications of providing barter/in-kind income to independent contractors and employees, provided that your attorney and accountant have considered and approved the arrangement.
Conclusion
Regardless of the approach you take, it's important to appreciate that barter arrangements have very real employment law and tax implications that should be carefully considered. This brief article is intended to introduce some of the key considerations under federal law, which can be a starting point for a discussion with your accountant and attorney. Please also note that state employment laws may have unique and different requirements than federal law, so state requirements should be assessed as well.