The drive system is a CVT gearbox which I have seen a lot of you use for diesel bikes...
So, if you took a working scooter (or one you know the CVT is in good health)
Fit the diesel engine in between your legs in a frame
Modify the scooter engine piece so you could run a chain and sprocket (or belt and pulleys) from the diesel to the crankshaft (or replace/modify the crank so its a straight shaft).
Would be a fairly easy and cheap method of a conversion.
Most 50cc scooters produce 3~6 hp and 125cc scooters produce between 8~14 hp depending on engine.
They all seem to use Kevlar drive belts now which are very strong yet small (less heat, same traction)
The one on the 50cc I was playing with had a V belt 3/4~1 inch wide and about 3/4 inch thick
I wouldn't recommend a large diesel, but a Yannmar (or clone of around 10hp should be fine)
And you could alter the acceleration/top speed by altering the sprockets and chain (belt and pulleys) from the diesel to the moped CVT.
Most 50cc scooters only rev to around 7000rpm so a 3600rpm diesel running a 2:1 drive the gearbox would equate to a similar speed
so the top speed would be around 40~50 mph depending on scooter, but it should get there quickly...
Just an idea I thought I would throw into the ideas pot
Any thoughts or questions?