TL;DR "stable genius" is a historic term which means a genius without mental disabilities.
The phrase "stable genius" did not originate with Trump, it is a phrase that has been in limited use since at least 1959, which is the earliest use of the phrase I could find. It appears, for example, in the book Starship Troopers written by Robert Heinlein in 1959 and is so far the earliest use of the term I can personally confirm.
...a neodog is not a talking dog; he is not a dog at all, he is an
artificially mutated symbiote derived from dog stock. A neo, a trained
Caleb, is about six times as bright as a dog, say about as intelligent
as a human moron — except that the comparison is not fair to the neo;
a moron is a defective, whereas a neo is a stable genius in his own
line of work.
Here we also get some context vital to understanding how the phrase is used. The quote explicitly uses the term stable genius to indicate that he is not a "defective". As we know "defective" was a historical term used to refer to individuals who had mental disabilities of some kind. So it is clear that in common usage a "stable genius" is intended to mean a genius without any mental disabilities. This may seem like an odd thing to say but when you think about it when you consider people like Autistics and people with Aspergers who can often present as a Genius in their own fields but still have some mental difficulties in other ways the use of the term becomes clear.