An air tank like you use to inflate tires would do it. You'd put a quick change chuck on the hose instead of just the tire inflation one, and then you could get a blower nozzle for it. You could just run by a tire shop and have them pump it full, and you'd have a ton of air...it'd be just like having a compressor for a good while.
It'd be a little bulky, but it's a legit alternative to actually owning a compressor.
And no, an air pump won't do the job.