I am surprised they are requiring you to have riding boots. I gave lessons and we did require a boot with a heel, but it didn't have to be riding boots. Tennis shoes are dangerous when riding as your foot could slide all the way through the stirrup and get hung up in a fall. A heel helps prevent this. There is a consignment place called "bits and pieces", but I don't have any info for them. You might try searching for it in local businesses on yahoo or something. Otherwise, depending on where you live, if you need western type boots there are several western stores- Cavenders, Western Warehouse, the Justin Outlet is in Justin- they usualy have irregulars pretty cheap. If you ned English, I'm not sure locally where there is an English place- the one big one I knew of closed! Petsmart with the horse stuff sometimes has boots.
Good Luck.