Hi, and welcome to rootschat.
A Walter Coleman and Caroline Cardall married October- December 1925 in Birmingham South district, if this looks like the correct marriage. (You do not say whereabouts your dad was born)
It may help to purchase this marriage cert. as it will have Walters fathers name on it hopefully
There are two marriages in Birmingham between 1930 1940 for Walter Coleman, but of course he could have remarried anywhere and there are a lot of Walter colemans around.
Any more info, however slight, that you may have will help.
Mike