Try doing a google search for the Harry Fox Agency. They usually deal in that kind of stuff.
Just from personal experience though, it ain't worth it to record someone elses song unless you have a label willing to go to the trouble for you.
I tried it once with a cover of 'Every Breath You Take' and the cost was up in the thousands of dollars to get permission and tons of paperwork involved.
I basically just gave up. A lot of it depends on how you'll be releasing the song and how many copies you intend to sell or get radio airplay.
And if it comes to posting it on the internet, forget it.... they don't even have a clue cause they're so far behind the times when it comes to giving worldwide permission.