Alex Carroll, the guru of Radio Publicity, offered this advice:

Most radio shows don’t book interviews any further than 2 weeks
in advance.

Furthermore, most radio shows take vacation starting Dec. 15-
20th and won’t get back into the swing of things until Monday,
Jan 7th next year.

That being said, I think your best bet is to send your
postcards out at the beginning of January. Normally you would
want to give them a little more lead time, but with the way the
holiday season schedule falls, I think if you send them out
before that they’ll just get lost in the holiday shuffle.

Alex maintains a comprehensive list of producers of radio shows. You can
learn more about this list and Alex’s training tools by clicking here.