www.scottishleague.net

From the Dumbarton book "The Sons of the Rock" by Jim McAllister 1954-55. Dumbarton team v Montrose at Links Park Rd 3 Oct 9th 1954 Murdoch, McKay, j Gallagher, Davie, Cadden, McCall, Anderson, Irwin, H Gallacher, Walsh, Auld. Lost 3-1. Anderson scored for Dumbarton 1955-56 v Inverness Caley at Bogh...

Just a thought. You could try a search on eBay for the match programmes and the year. You don't have to bid for them and it might give you the dates.