Ardsley has a swim program for kids age 4-15. Its $185/session. Next session starts Feb 9 and ends 5/3. Sessions are 30 minutes long and occur on Saturdays. However, Ardsley may be far for you. It will probably be a 15-20 minute drive.
I heard that the JCC in Scarsdale has a program too. Not sure if you have to be a member or if you have to be Jewish to go but a co-worker took her kids here. I think they offer private lessons too.