This seems to be a little better, benchmarkwise (it assumes days are numbered 0-6):

use strict;

# Days start at 0, just like arrays
my $start_day = 6;
my $days = 7;
my @cnts = daycounts($start_day, $days);
for (0..6) {
 print "$_: $cnts[$_]\n";
}
sub daycounts {
 use integer;
 my $start_day = shift;
 my $days = shift;
 my $end_day = ($start_day + $days) % 7;
 my $compare = ($start_day <= $end_day)
  ? sub { my $num = shift; $start_day <= $num and $num <= $end_day }
  : sub { my $num = shift; $num <= $end_day or $start_day <= $num };
 my @adjust = map { $compare->($_)? 1 : 0 } 0..6;
 my $cnts = $days / 7;
 map { $cnts + $adjust[$_] } 0..6;
}
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Update: There. fixed. Except now its slower :( though if you unroll that sub reference/dereference and map into two separate maps then its faster :)

Another update: Re:ThuG's reply - I made the assumption that zero days means just the start day, and 1 day means the start day and the next day, so 17 days from Wednesday would take you to Saturday, not Friday. So just subtract one from $days coming in to get what you expect.