As a guy who worked in radio for 20 years (though it’s been almost 20 years since), I’d have to tell you that there ain’t no free lunch. You can’t even buy a bunch of CDs and put the music on the air without paying an annual blanket royalty fee to BMI, ASCAP and SESAC so that the composers of the songs benefit.
There are many syndicators out there who will be delighted to sell you the rights to broadcast in your market their package of old time radio shows. In addition, I suspect these days that they may have a satellite-feed network doing the same thing, as every other format under the sun is available that way.
At our small market radio station in Oregon, we bought a package of 20 classic radio Christmas shows including the rights to broadcast those 20 shows in our market only for perpetuity. Great stuff, including Jack Benny, Duffy’s Tavern, Burns & Allen, etc. and it was easy to get local advertizers to sponssor their very own show. We used to schedule a block of them on Christmas Eve and Christmas Day and had good audience response.
Doing it full time would be a lot of fun, but also sounds like a lot of work.
As a practical matter, you would probably need a top 50 market to find enough listeners who like that particular format to make an audience large enough to sell to advertizers. Small town stations generally have to go either to a very broad appeal format (generic country or generic rock or news/talk) or segment the hell out of the dayparts and try and get a chunk for everybody. At a very small market (250 watt local AM) where I started back in the mid-60s, the owner provided a general middle-of-the-road format (Andy Williams, Tijuana Brass, 101 Strings, etc.) and threw in lots of specialty shows. There was a kids’ “Fun House” program that aired after school at 3:30 with the kiddie records of the 50s that featured Tubby the Tuba, Gerald McBoing-Boing and a few old transcribed network radio shows (“Buzz Corey and the Space Commandos”).
Then a Teen Tune program from 4:30 to 5:00, lots of wire service news, an hour of “dinner music” from 6:00 to 7:00, mostly strings or piano music, a Polka Party on Friday nights, a Request Time on Monday Nights, four hours of classical music on Sunday night, etc. It was a small semi-isolated market, and the owner wanted to put something on for everyone.
It was the kind of station where we read obituaries on the air because the local newspaper was a weekly and it would be possible for someone to die and have a funeral scheduled before the paper came out again. so we aired funeral notices including obits as a public service so people would not miss out.
Good luck on your venture