I'm pretty sure that there is no constitutional bar on someone convicted of a felony, or even still currently serving time for that felony, also being president. There is an obvious logic that someone with a criminal felony could be allowed become president, because someone could be convicted in a way later viewed as unjust (e.g. think Nelson Mandela). The president must be barred from holding public office by Congress (i.e. impeachment), not a standard court.
There are articles that could be interpreted as making it impossible for someone in prison to be president - for instance being in prison could be argued to mean that the president is unable to discharge the duties of office. However, who gets to decide that? If Congress, with at least a third of the senators Republican... Mmm.
Would Trump try to pardon himself? I'd like to think that can't stick. Can Trump stand down and make his VP president, the new president pardons Trump, appoints Trump the VP, and then stands down themselves to return the presidency to him? Shenanigans, but if Congress is unwilling to call on it, it may legally stand.
This is the territory of a constitutional crisis. And why I strongly suspect it's not going to come about, because if people really have to face the reality of a convicted man becoming president, I suspect enough of them will get cold feet.