McCoist's men take on their part-time rivals in front of the Sky Sports cameras in the quarter-final replay at New Douglas Park this evening.
The Glasgow giants were fortunate to earn a 1-1 draw at Ibrox eight days ago after struggling to break down the Coatbridge club's packed defence.
And McCoist expects James Ward's side to adopt exactly the same ultra-defensive approach despite being at home tonight.
McCoist said: "Watching them against ourselves on Sunday, and having watched their previous games against Stenhousemuir and Motherwell in particular, they played the exactly same shape. I don't see them changing it."
He added: "I think they'll set up the same way with the 4-1-4-1 with Ciaran Donnelly sitting in front and will be extremely difficult to break down once again."
After conceding a soft goal early on in the first game against Albion Rovers eight days ago, Rangers battered their League Two opponents.
But it took a highly controversial equaliser from Bilel Mohsni late on to scrape a draw.
McCoist knows his charges will have to be far more clinical in the final third tonight to book a semi-final slot against Premiership Dundee United at Ibrox.
And with so much at stake for the cash-strapped Govan club, he says the meeting with the Cliftonhill minnows is "arguably our biggest game of the season".
The manager said: "We will gave to be a lot sharper on the ball than we were last Sunday.
"Now we have an opportunity to put things right, but we'll have to do things a lot better than we did in the first game in terms of taking our chances if we want to win."
Meanwhile, McCoist thanked fans for their continued backing following the 2-0 win over Dunfermline - but declined to comment on their show of support for Dave King at the Scottish League One match.
The majority of the Ibrox crowd held up blue cards, distributed by The Union of Fans, on 18 and 72 minutes to back reinvestment by the former director.
The South Africa-based businessman is in Glasgow for talks with the board and fans groups.
McCoist is due to hold crunch talks with chief executive Graham Wallace this week.
And he admitted King would probably be on the agenda.