The duo were crocked in yesterday's 2-1 win over Brechin that extended Rangers' lead at the top of the League One table as goals from Fraser Aird and Nicky Clark clinched the points.
McCoist's side face Raith Rovers in the Ramsdens Cup final in a fortnight before Dundee United head to Ibrox for the Scottish Cup semi-final, with the Light Blues boss already facing the prospect of being without David Templeton and Andy Little for a crunch few weeks.
McCoist said: "Nicky has a twisted back and Ian has got a really sore one with the blocked tackle. Obviously, it's far too early for me to talk about their injuries, but they will certainly be assessed in the next 24 hours and we will keep our fingers crossed because as you can imagine, it's not ideal.
"There's a good bit of football to be played before the Dundee United game. But Temps and Andy Little, their scans are not too encouraging, and that's more injuries to other key players because those two [Law and Black] have certainly been our central midfield for the majority of the games this season.
"Black has caught the lad's foot as he's attempted to hit it. I was surprised he went for it, to be honest, because I couldn't see it ending in anything other than tears with the way the boy was coming out to block it, but he went for it and attempted the shot and that's what it was, just a block."
The loss of Law and Black would be a huge blow to Rangers at a crucial stage of the season as they look to end the campaign on a high and land a silverware hat-trick.
Youngster Lewis Macleod is also out of action just now and hasn't featured since January, but McCoist is eager to see him play his part.
He said: "I'm very hopeful. Lewis has a viral problem. Obviously, that's well outwith my league, but listening to the doc and the specialist, who he went to see last Thursday (he expects a positive outcome).
"The results haven't come through yet, nor has his previous tests. But the doc will chase them up this week and he will be going down to see another specialist towards the end of next week."
The positive on what could prove to be a costly day for Rangers was the three points from a hard-fought encounter.
And McCoist hailed the impact of goal hero Clark as he netted the winner at Glebe Park for the second time this season.
The Gers boss said: "He made the difference. As crazy as it may seem, we might have been better starting with him because he gave us a run-through against the wind. He made a real impact the last time he was here and he certainly changed the game again, there's no doubt about it."