Presuming your code was copied correctly, it's not syntactically correct: you're missing the closing slash after the $1. When that's corrected, if I read it correctly (a very big if!), you'll just replace the year and everything to the right of it by the year, and the trailing blanks.

Try this:

#!/usr/bin/perl

use strict;
use warnings;

while(<DATA>){
    chomp();
    print "before: $_\n";
    s/(\d+\s+)(.+)/$1 (Birthday) $2 - singer/;
    print "after: $_\n";
  }

__DATA__
January 1, 1915      Franck Pourcel
January 3, 1926     George Martin
January 3, 1945     Stephen Stills
January 3, 1946     John Paul Jones
January 4, 1942     John McLaughlin
January 5, 1950     Chris Stein
[download]

I think this will make the change you want; the regex is the important bit.