Even if every single news site went down on election night, it would be fine. People aren't gonna die if they don't find out who won the election until the next day or even the next week.
The fastest state to certify actual official results takes 2 or 3 days (Delaware), and most states are closer to 2 or 3 weeks.
And then...
Directs the military to strike on [target] and the military says "Not my Commander" and no strike is carried out.
There is no Coup unless the powers are transferred.
It cannot happen.
The President remains Commander in Chief for several months, from November until late January.
(And now enjoys absolute immunity for official acts performed under that hat.)
In such a case, it'd be a https://en.wikipedia.org/wiki/Self-coup
Not all coups are military.