I use an external battery/jump-starter with a built-in inflator. Of course you have to remember to recharge it after use, and just in general charge it every month or so to keep the battery inside happy.
I'll be honest, I've never successfully jumped my modern vehicle with one; not sure if that's due to insufficient capacity, pilot error, or if they just don't work well for modern cars? But they're still very handy for other purposes, including charging/powering smaller devices while the car is turned off.