Programs to help low income families to pay for sports or organized hobbies?

Try doing a search at Volunteer Match, or your local United Way 2-1-1 referral service, or try the county Recreation department, and local arts and sports associations.

I'm not aware of any grants that pay for individual classes or leagues; but there are youth sports and arts programs available from several organizations.

I found this one on VolunteerMatch:

ARTS (A Reason To Survive)

http://www.artsurvive.org/outreach.php

Check out local YMCAs, 4-H clubs, Boys and Girls clubs, your local recreation department (city or county), Boy or Girl Scouts, and local arts and music groups.

None of that is productive for kids. It's pure entertainment.

If you want to do something productive, look for a program that pushes math or science skills in kids. Everything else is worthless fluff.