A private college can set the rate of pay.
See Coaches and the teacher exemption under section 13(a)(1), January 15, 2009 Fair Labor Standards Act.
There is no need to pursue this further. Extracurricular wages are routinely paid as flat amounts, whether in grade school high school or college. You are under contract to do a job for the wage agreed upon. If you are dissatisfied with your pay, don't renew your contract.