It has been a difficult debut pre-season campaign for Moyes, who is still to make his first significant summer signing and won only two of six tour matches.
Sunday's Community Shield encounter with Wigan at Wembley does offer the obvious chance of some silverware, yet Moyes is acutely aware of the tough start that follows, with Chelsea, Liverpool and Manchester City all to come in the weeks immediately after an opening day trip to Swansea.
Coyle has no concerns though. He has watched Moyes' career develop closely. And he feels United have the perfect man to replace Sir Alex Ferguson.
"David has succeeded Sir Alex on merit," said Coyle. "For years I have been saying he could manage any top club in world football.
"There is no doubting what he has done.
"He has been at the coal face with Preston and earned the right to go from there to Everton, where he also did a magnificent job.
"He was a natural successor to Sir Alex and it is great to see a home-grown manager evolving to that level. I have no doubts he will have huge success at Manchester United."
Sunday will be the first time since the 1985 Charity Shield that United have played a game at Wembley with someone other than Ferguson as manager.
It may take a bit of getting used to, even for Coyle, who will be standing alongside Moyes on the touchline.
"Sir Alex was there for a long time, particularly for football," said Coyle. "The way football works, that time is probably worth 10 times that amount in any other walk of life.
"Will it be strange? Maybe to begin with. That is only natural. But when you see the stature of the man who is there, you know he is the right custodian for Manchester United."