I'm curious if there is a relatively cheap, small (portable), simple piece of equipment that I can use to give my voice an echo when I'm on the air at my local FM radio station?

We use high quality Senheiser mics with unbalanced jacks (not RCA) that go into the board.

I guess my ultimate fantasy would be to have something as small as a guitar pedal effect, battery operated, that I could just plug in downstream from the mic. I'm clueless as to what is possible today, as I stopped following what was happening in sound/music equipment many moons ago. Any suggestions are appreciated. Thanks.

There's things like a Boss Digital Delay pedal which is guitar pedal size and you can probably pick it up for cheap on ebay.