Further to Lawrence B. Crowell's excellent answer above: in the past, Jupiter was often described (temptingly but mistakenly) as a failed star. It's not even close to the mass needed for self-ignited fusion, and dropping e.g. an Earth-mass mini black hole wouldn't light or sustain nuclear fusion. The mass would still be too low.
However, supposing you could corral a mini black hole and nudge it close enough for Jupiter to capture and swallow it, the black hole would generate huge amounts of energy by consuming anything and everything that dropped into it, but it would also generate a tremendous counterpressure that would prevent its swallowing Jupiter at a gulp.
After oscillating countless times and who-knows-how-many years, the black hole would settle in the center and eventually (inevitably) suck nearly all of Jupiter into itself, all the while producing gobs and gobs of energy that might or might not be useful to anyone. Because of the counterpressure, the process would take a very (I mean a very) long time, but it wouldn't be fusion. For that you'd need enough mass for at least a dwarf star, whether brown, white, or lavender.
[Edit/afterthought]: Only two candidate Earths? Have your forgotten dear old Mars? Incidentally, Jupiter's existing magnetic field pretty much rules out the possibility of ever establishing a human presence on Jupiter's biggest, most succulent moons. Alas for Robert A. Heinlein's 'Farmer in the Sky'...