Black is set to play against Stenhousemuir this afternoon at Ibrox after a three-match suspension.
The midfielder admitted to a string of gambling offences to the SFA - including backing the Gers not to win.
And despite one Light Blues fans group calling for him to be sacked, Rangers boss McCoist is hopeful supporters get behind Black.
He said: "There's every chance Blackie will start. He's a big enough lad to handle himself and speak for himself.
"But I'd be very hopeful the attention on him now will be for the way he is playing.
"I'd be hopeful we can put everything to the past and he can recapture the form he was showing before the suspension.
"I want to be talking about how well Ian Black is playing.
"I'd like to think he would get a good reception. The Rangers fans have been phenomenal in their support of the team and the club in the last two years.
"We are thankful for that and proud of that. They have always got behind the team and the players and I'd hope that will be the case.
"I don't see anything changing. I hope we can put it all behind us and move on."
McCoist added: "We have said he was wrong and punished him internally. He has come out and apologised and has served his punishment.
"Football divides opinion all the time, especially at this club in the last two years.
"I get stick myself about performances and team selections. It's part and parcel.
"We can't take our eye off the ball for that long-term."
McCoist will be without Seb Faure for the visit of third-placed Stenhousemuir to Ibrox this afternoon.
The Frenchman suffered a neck injury in a closed-doors game against Partick Thistle in midweek.
But Lewis Macleod, who missed the SPFL League One game against Forfar last weekend, is set to slot back into the line-up.
The match is still too early for Kyle Hutton despite the midfielder returning to training.