The Light Blues got their first SPFL Championship points on the board with victory over Falkirk last Friday before hitting the goal trail and blasting eight past Clyde in the Petrofac Training Cup this week.
It has been a poor start to the season for their opponents tomorrow, however, with Ian Murray's side losing to both Raith Rovers and Queen of the South in the opening fortnight.
And McCoist is determined to add to the Sons' sorrows at Ibrox as the League One champions look to build some momentum for their title challenge.
He said: "It's a game we are looking forward to. I was down at Dumbarton last Saturday and saw Queen of the South win 4-0.
"They will obviously be looking to do a lot better than that and it was a bad day at the office for them.
"I don't like to comment on other teams because that's other managers' jobs but I'm sure Ian will admit that.
"It was the first time I've seen Dumbarton have a bad day at the office and I've seen them a good few times. They're a far better side than they showed last weekend.
"They will want to make amends for that and they've got experience in their side. They've brought in David van Zanten and Lee Mair, while big Colin Nish is up front.
"It has been a tough start to the league campaign for Dumbarton and they will be very eager to start picking up points, but we'd like to continue winning."
While Rangers romped to the League One crown last term, Murray took Dumbarton to the brink of a Championship play-off spot as the part-time team defied the odds in the second tier.
The former Light Blues defender has emerged as one of the brightest young managers in the country as he has transformed the Sons' fortunes.
And McCoist is pleased to see the 33-year-old enjoying success on the other side of the white line.
He said: "Dumbarton is a great football club and Ian is learning his trade down there. I thought they did really well last season.
"They held their own and played some good stuff. That's obviously down to the work the coaching staff did.
"I know Ian's assistant, Jack Ross, is away to take the youths at Hearts and maybe that has been a little bit of a blow to him.
"At the same time, Ian is certainly one of the more respected younger coaches in the country and this just the start of what I'm sure will be a great career for him in that department."