Hi:
I have produced several "copy" albums and I have the info you need. First, your best reference for all things related to paying royalties is the Harry Fox Agency, and their FAQ page is here:
http://www.nmpa.org/hfa/hfafaq.html The statuatory rate currently is 8 cents per five minute song per copy. You cannot license less than 500 copies. You can do the math but if you do a copy album of ten songs then you will have to pay 80 cents per album or $400.00 per 500 albums.
The way you pay royalties is easy: go to
http://www.songfile.com/. This is where you should go first and look up the songs that you want to record to see if they are available for mechanical licensing through HFA - not all are. If the song you want is not available for licensing through HFA, either you cannot record it or you'll have to work out a special deal with the individual song's publisher. If licensing is available for the song through HFA, you fill out a form for each song and pay your fees all on-line. Be sure to make note of the publisher and the song author(s) because the credit information has to be printed on your album cover. You will get a license certificate in the mail.
I know you didn't ask this but just FYI: you can copyright a cover album, or more specifically you can copyright your actual recording, arrangements and production. The website for info and forms is:
http://www.loc.gov/copyright/