Thoughts;
a) Improvised Tourniquet - which might take some MIGHTY force and help from someone able to inflate the tire while you hold the tourney.
Listen VERY CAREFULLY for any sounds that might indicate the tourney is letting go, e.g. fabric tearing type of sound if you are twisting up a strap.
b) Inflatable band that is strapped around the tire, then inflate the band.
I don't know the proper name for these, except that tire places use them, I also have no idea of cost, probably depends on the size. You MIGHT be able to borrow or rent one.
c) Starter fluid, I know construction guys who swear by this as the only way for large back-hoe size tires. The thought of this scares the heck out of me, but so do a lot of things that guys do on construction sites.
It takes a LOT of air to get a car tire on, most of us don't have air tanks big enough or hoses fat and short enough to do it. Tractor tires take a lot more, obviously.
What size tires are these anyway ?
(just curious).