I am certain that I am missing dozens of these, but here's a sample of radio stations (primarily community and freeform stations) that are organized primarily around shows and that have an archive of those shows (typically two weeks) online for on-demand listening.
If you can't tune into your favorite show, either because it's out of market or at the wrong time, this is a place to start looking around.
My favorites
- WCBN Ann Arbor: https://floyd.wcbn.org/listen/indexbyn.html
- WWOZ New Orleans: https://www.wwoz.org/about-wwozs-two-week-demand-archive
Others that I have found
- WDIY Lehigh Valley PA: https://www.wdiy.org/two-week-music-show-archive
- WDCB Chicago (Jazz): https://wdcb.org/archive
- WGDR Central Vermont: http://archive.wgdr.org
- WUMB Boston (weekend programming): http://50.241.124.209:8080/cgi-bin/archive/archive1.pl
- KHEN Salida, Colorado: https://archive.khen.org
- KMUN Astoria, Oregon: https://kmun.org/archives/
- KSQD Santa Cruz California: https://ksqd.org/two-week-archive/
- KUPR Placitas New Mexico: https://www.kupr.org/archives.html
Thanks to WCBN's archive of Brian Tomsic's "Train to Skaville" show for the accompanying music for this search.