Hi L.,
I don't know of any center where you could take your baby for swimming lessons, but I can tell you about my experience.
When my daughter wasn't even 6 months old, I enrolled us (my husband join us too) in a three month swimming program.
It was in a YMCA in New Jersey.
Parents and babies had a once a week 45 min session with a trainer.
We would sing songs while moving around in the water, play with floating toys, practise a few exercises and just enjoy some free time with our baby.
I was afraid of having to let go of my daughter and let her swim under the water (something that very young babies do naturally, they just block their breathing and enjoy the experience without fear) but I wasn't forced to do it.
Anyway, we had an amazing time, my daughter loved it just like any other baby in the group and we especially cherished our first real activity together.
One last thing, my daughter will soon turn 4. She is like a fish in water, has always been since the swimming lessons. Does it have something to do with the lessons? I have no doubt.
I can only encourage you to do the same, you will love it, it's very relaxing.
All the best,
F.