You can shoot butane gas into a tire that's come off its rim. After igniting it, it gets surked onto the rim by creating some sort of vacuum, I presume.
You can use non-aerosol fuel, too, although you risk melting or burning the rubber.
Make sure you follow up by inflating the tire, not by sucking its cheeks back in.
Short and sweet.
Of course, sometimes it all goes horribly wrong.