Choosing a Solid State Relay for an AC air compressor application
Finding a suitable SSR should be fairly easy based on your requirements. Look on amazon, ebay, and automation direct for reasonably priced options.

Parameters:


Input voltage, and DC or AC. You want DC. Most DC ssrs have a huge input voltage range like 3-60v or similar.
AC or DC output. You want AC.
Zero crossing or not. This only applies to AC output SSRs. Just get zero crossing unless you know otherwise. Zero crossing minimizes the heat generated during switching by waiting for the AC voltage to hit 0 to switch. The only time you don't want this is if you're creating some kind of wave chopping dimmer circuit.
Current rating. High current SSRs are cheap, so give yourself some margin.