Hey Dave,
Welcome to the bloody knuckle hissy fit club!
I can't imagine a 50cc bike causing much trouble, but I will take your word for it. It's all down to good technique. If you're having trouble breaking the bead, then I'd recommend a few things:
I use a big "C" clamp to break the bead. Works well even on stiff, steel belted tires. I put a couple little wood blocks to spread pressure on Clamp. Works well even on very stubborn tires.
Some guys can break even stubborn beads just using 8" tire irons and somehow wedging them in, working them around the tire. I've tired using bike side stands, car jacks and long 2 X 4 lever set ups, all with MIXED results.
On side of the road you will be limited. The C clamp works but is HEAVY and LARGE ... but many other solutions out there.
Another popular tire Iron now used are the Motion Pro ones:
BeadPro Tire Bead Breaker and Lever Tool Set
BeadPro FS (Forged Steel)
The long (16"), steel irons best for home/shop use, the Alu are 10" long, perfect for packing on the bike. These require using them in tandem to create a lever and POP the bead. Videos are about on the net showing how they work.
I don't own these but a friend did a change with them (short ALU ones) on his KTM 950 rear tire and they worked a treat. Impressive, and faster than using my BIG heavy C clamp. I will buy a set of Alu ones at some point. Best I've seen, and work for getting tire on and off as well.
I don't have much trouble once bead is broken, goes for removing tire/tube and getting all back on. I carry rubber lube on board called RU GLIDE. Many brands for sale, Motion Pro sells everything for tire changes.
At home I have a set of 16" irons. With these you really have to be careful, you can break the steel bead in your tire or can damage your wheel badly ... I'VE DONE BOTH!
One trick I like is using BIG HD plastic Zip Ties to clamp tire together. This helps to force it deep into tire Well easier, allows you to lever tire on opposite side. Keeping tire deep into tire "well" is key to getting tire on easily, even with short 8" irons.
Less chance you will pinch your tube as well.
SMALL BITES ONLY!
Also, never get greedy when levering on tire. Take small bites and keep constant pressure to force tire deep into Well as you work round the tire. Multiple Irons best for me. A buddies BOOT can help too to force tire into Well as you work round.
One important thing many forget!
ALWAYS REMOVE VALVE CORE FROM AIR VALVE STEM. If you don't do this ... you will never, ever break the bead. (but might break tire or wheel!) Let new tires sit in Sun or bring inside.
I carry 3 tire Irons. (essential, IMO) But whenever possible I let a tire pro do the work. Thing is, the more you do it, the easier it gets. It's still a terrible, bloody job. I've been on Baja rides where we had 5 flats in a day. Really sucks, eats up riding time badly.
We had one guy on one ride who was a ISDE level guy, could change a tire in under 5 minutes if plied with Beer! Me? A good half hour if things go well.