You should be able to go to your auto parts store of choice and get a belt. You're not looking for a unicorn here, since I believe all Vibes came with A/C as a standard option. If there are any that don't, then they are the unicorns and hard to find.
Assuming you've got a Base (1ZZ w/ Automatic or 5 speed) and not a GT (2ZZ w/ 6 speed), then here's a compatible Gates belt from O'Reily's:
https://www.oreillyauto.com/detail/b/ce ... belt&pos=2
ColonelPanic is correct. The Vibe's belt is different from Matrix and Corolla, even though they have the same engine options. The A/C compressor was different, because GM decided to use their own HVAC system instead of the Toyota system.