Sometimes you can find a special planet with an "artifact" called "Crazy Paul's Space Port" where you can get a buy 1 ship, get 2 ships free deal when you build frigate factories there.

I'm just messin' with ya.  If you're Vasari you can research an ability that will increase your max fleet supply by 15%.  If you're TEC and you enter into diplomatic pacts you can get a large max fleet supply increase for the final pact.  (If you're playing another race, you can get it if a TEC AI enters into a pact with you.)

Definitely the Phasic Transmissions research subject for Vasari. TEC Pact, however, gives 800 more supply regardless of how many fleet upgrades you've performed.