There are 6 private high schools on Long Island that compete in the New York Catholic High School Football League [NYCHFSL] along with other private schools in NY; mostly New York City. The NYCHSFL is comprised of three leagues (AAA, AA, A). They have an informative website where you can find schedules, scores, stats, etc.
For Pete's take on the NYCHSFL click here. This is a great blog which covers all teams in depth.
Long Island Lutheran located in Brookville also has a high school team and plays an independent schedule. Click here for more info on their football team.