I used an older Netgear router. Turned off DHCP (and any other router type functions I could find, though I don't recall if there were any). I connected an ethernet cable from the main router to one of the output jacks (don't use the jack that connects to the modem when you're using it as a router). The thing just acts like a switch, but of course it has wireless capability.

I set it up for channel 11 (the main router uses channel 6) and a different ID (forget what it's called, and I don't know if it's necessary. It also has its' own static ip address).

Since most routers also have 4 ethernet connections, I have 3 left over for printers, etc.

I see no reason why it can't be used to connect wirelessly to your existing router, but if you had a good signal where your printers are, you wouldn't need this in the first place.

I have a box full of old routers - if I had to buy something, I'd most likely get one of the devices specifically designed for this purpose, as mentioned upthread