Reddit mentions of Cylinder Kit 50cc 2 Stroke 10mm Piston Pin Yamaha JOG clones Minarelli 1E40QMB Engines (0108)

Check Trademe.

Buy something Japanese if you want it to be reliable and not rust to pieces but the Chinese and Korean ones will get you from A to B for a limited amount of time (they'll last longer if you keep it in a garage) for a relatively small amount of money. A Yamaha Jog is one of the faster 49cc ones (one of the very few that can actually make it to 60KM/H). Buy a Piaggio, Vespa or Peugeot if you're bourgeois.

Make sure you get a nice full face helmet that fits you well and some gear. Cars don't discriminate between hitting people in gear and those that are not; better to leave the altercation with your face and skin than without. Definitely recommend getting a helmet with an internal sunvisor. For one, they make you look like robocop, but they're also invaluable for commutes when the sun is low in the sky.

4 stroke engines like those in the Honda Today are reliable and run a long time but they're slow as fuck and no fun at all (seriously, can barely make it to road speeds, which is both dangerous and a liability to other motorists).

2 stroke engines are faster, but they require topping up the oil as you top up the petrol and they also require the top end to be rebuilt periodically. They will eventually seize and ideally you will rebuild it before it seizes. If you buy one that is reaching 40,000KMs, plan on rebuilding it. It's not as difficult as it sounds. You just get a kit like this (which is one for aforementioned Yamaha Jog) and you take some parts off and replace them; or just don't get one with that much mileage. They also smell delicious; it will grow on you.