I've never seen any places offering rental gear, unless it is already in rehearsal space when you rent it. The venues that do offer it only offer rental of PA, lights and crew, not amps or cables.

I've talked a bit more with them, and they seem nice enough. I'll give them a shot, and see if it works out. They don't seem to mind that my amp is a Fender Mustang. "We can always mic it", as their bassist just wrote in a text message :)

The only problem is a few effects, but those aren't a requirement. They would be nice to have in stompboxes, but I have the most important ones, and the rest can be found in the amp, when it comes to Rhythm parts. They're also only looking for one guitarist, and since the Wikipedia definition of Stoner Rock says it's slow-to-mid-tempo riff-based rock, it sounds like it's perfect for me, even though I don't like Bass-Heavy music that much. Of course, their definition may vary from the Wikipedia one.