Building on a couple of the answers already posted. The Zero-width assertion allows you to do a regular expression match without placing those characters in the match. By placing the first part of the string in a group we've separated it from the digits that you want to be replaced. Then by using a zero-width lookbehind assertion in that group we allow the regular expression to proceed as normal but omit the characters in that group in the match. Similarly, we've placed the last part of the string in a group, and used a zero-width lookahead assertion. Grouping Constructs on MSDN shows the groups as well as the assertions.
resultString = Regex.Replace(
im_cfg_contents,
@"(?<=\$displayHeight[\s]*=[\s]*"")(.*)(?="";)",
Convert.ToString(y_res));
Another approach would be to use the following code. The modification to the regular expression is just placing the first part in a group and the last part in a group. Then in the replace string, we add back in the first and third groups. Not quite as nice as the first approach, but not quite as bad as writing out the $displayHeight part. Substitutions on MSDN shows how the $ characters work.
resultString = Regex.Replace(
im_cfg_contents,
@"(\$displayHeight[\s]*=[\s]*"")(.*)("";)",
"${1}" + Convert.ToString(y_res) + "${3}");