I'am slow learning how to use this winamp program, but so far found a long list of available radio stations that is searchable using keywords, and for my oldies of the late 50s early 60s I only found one station, but its 50s - 70s.
I just tried the above radio-locator web site and glad to report that its easy to use. I entered UT for a state and it listed lots of web radio stations, so I hope eventually I can find that one long ago that played only late 50 - early 60.