No, as you suspect, s/// doesn't work like that.

How about something like:

use strict;
use warnings;

my (@config);
push @config, 'line 1 oldtext appears but once here',
              'line 2 oldtext is here twice oldtext',
              'line 3 oldtext is here oldtext three oldtext times!';
for (@config) {
   my $count = 2;
   while ($count-- && s/oldtext/newtext/) { print 'Replaced '}
   print "\n";
}

print "$_\n" for @config;
[download]

Output:

Replaced
Replaced Replaced
Replaced Replaced
line 1 newtext appears but once here
line 2 newtext is here twice newtext
line 3 newtext is here newtext three oldtext times!
[download]

Update -- some explanation:

The print statement in the while loop is to provide a hint about how this works. We're taking advantage of a couple facts here: (1) s/.../.../ will only perform 1 substitution at a time, and (2) s/.../.../ returns the number of substitutions it performed (either 0 or 1 in this case). I set $count to the maximum number of replacements I want to make.

For the first line of the array, the while loop runs only once. Even though $count at that point is 1, the s/// returns 0, and that makes the while condition false.

For the second and third lines of the array, the loop runs only twice, and that's because $count has counted down to 0.