You could try:
$line =~ s!$/+!$/!sg;
Note the replacement of / with ! in the regex. This is perfectly allowed and allows te easy use of \$.
In my opinion this is better than s/\n+/\n/ as it allows for the possibility that you line terminator $/ has been set to something else (admittedly, this must be done explictly by you). However taking this approach is a safer option from the point of view of bugs being introduced if you bury s/\n+/\n/ in a library and then start getting random errors from users on the basis they have chnaged \$. I'm not however advocating that what I just said doesn't have a counter argument that works the other way.
Arun