the problem with that is any diesel engine you find will be 1 of 2 things. it will be to big, or too heavy. the reason for this is that it should be difficult to mate a diesel to a transmission on a small 250 bike frame. to compensate for lack of a trans, you need a bigger engine capable of putting down enough power to overcome less than ideal situations that would otherwise be solved with a transmission. the problem with bigger engines is weight. 250cc dirtbike motors are light enough anbd small enough to pick up with one arm and set up on a benchtop.
you could maybe use a snow mobile variable pitch belt setup, but you would need to mount it to a jackshaft which adds complexity.
if you just want someting like a pitbike to cross parking lots or very light duty use, then any little diesel with a gocart clutch would work good, no jackshafts or variable pitch clutches needed. just install a centrifucal gocart clutch and hook up a chain to the drive wheel. i see alot of pit bikes made like this, although none are diesel.