For fronts, I'd have slimed it. That's what I did the first time one of my fronts went flat. Think a bottle of slime that'll do both front tires only costs about $12.
I used to open my Dad's service station on Sunday afternoons, and he'd let me have all the profits. Biggest profit maker back in those days was flats by the Sunday drivers.
Also back in those days, there were very few tire machines. So, I did everything with a bead breaker and a couple of tire irons. You can still buy those same bead breakers on the internet. They're just an L-shaped gizmo with the top part of the "L" having a projection on which there is a hinge. To that hinge is affixed a bar that goes down to a half-moon-looking piece of metal that mates up with the tire where the bead goes against the underside of the rim. All you do is let all the air out (usually flat already) and push down, rotate, push down, etc. until the bead comes loose from the rim. Do both sides. Prior to this, if you haven't located the leak, you need to reinflate the tire and find and mark the leak.
You need a straight tire iron and one that looks a little curved on its flat end, like a spoon. Use the curved one to get behind the rim where the bead was and behind the rubber bead. Lever the tire bead up over the outside of the rim. Then use the straight tire iron to remove the rest of the bead, working your way in little bits around the bead. For bicycle tires, a couple big screwdrivers work fine.
To remove the tire entirely from the rim now, position that curved iron again and either work your way around the bead with the straight one again OR you can whack the tire at the bead with a rubber mallet while you push the opposite direction on the rim. This was often faster than working your way around the rim with a tire iron, once you've mastered where to whack.
Do your tire repair. This can be done with a cold patch or with a big "C" clamp to hold a hot patch in place over the leak spot.
Now, to get the tire back on, I'd usually hold the rim in place with one foot with the tire held by both hands and whack it onto the rim to get it "stuck" to be able then to work my way around the bead with the straight or the curved irons. You can "stomp" it on, too, if you've big feet. With smaller tires, you can usually secure the bead in one spot with an iron and work it on with the other. The outer bead then is a bit easier to get started and levered back inside. It gets a whole lot more complicated if you have a tube. Gotta make sure you don't pinch the tube. May have to partly inflate the tube to keep it from getting pinched, etc. particularly if you've putting a split rim back together.
With small tires, and even big ones, you can break the bead loose with a large chisel and a hammer or even a large screwdriver and hammer if the tire is really small. Then work around the bead with an iron to get it over the rim. We also had an impact chisel that was a huge long tube with a big chisel on the end and a cylindrical weight inside that we used to break beads, particularly on big truck tires.
Really small tires sometimes are a "*****" to get the bead broken and resealed. I've had to use a tension strap around some of these little buggers to get them to reseat. BE SURE and remove the tension on the strap before you get much pressure on the tire though. It often helps to remove the valve "core" (the Schrader valve inside the valve stem) when putting air into a tire to reseat it. Even helps to do this on tubes, remove core, inflate a bit, let out air, put core back in, inflate. This helps to keep the tube from being inflated with folds in it that can cause crease holes. (If there's a way of screwing up any of these operations, I've done them. What I'm telling you is ways to avoid the screwups. Having customers return after you've fixed their flats ain't too much fun.)
Hope this helps. I made lots of money fixing flats on Sunday afternoons. Think little tires on either split or unsplit rims are almost the biggest challenge, particularly the ones on dollies or wheelbarrows.
Ralph