Not sure how it works in the city, but a lot of towns do them through the recreation departments. Especially in the summer. I know our town (East Aurora), and probably most others have rates for non-residents too.
I will say though, I have been WAY happier with the Y swim lessons than I was with the town ones. There are less kids so the instructor can work with the kids a lot more, and I just like the style of them better.
We did lessons at Summit Fitness Center almost to Niagara Falls. To far for you, but there might be a local gym with a pool that does kids lessons. There was a fee for gym member's kids and for non-member's kids. (I'm a non-member.)
I actually picked up the family fun free magazine at my library and the lessons were listed in one of the ads.
The Town of West Seneca offers a class through community education.
It's open to non-residents too. We took DD last year, and while she hated the water - it was a great program.