Bribery laws wouldn't apply IMO to anyone involved. Unless you want to stretch that public school coaches into being government officials, but that doesn't pertain to the private school coaches.
Paying someone money in of itself in the private sector isn't against the law unless it defrauds people. Also how is paying a kid in cash different than paying him in tuition?
So who exactly was defrauded here? Just the IRS IMO. Had these guys claimed the money on their tax return but hid the income from their employers, they would be out of a job but also out of jail.