The trick is that the last day of the month is the day before the first day of next month. So here's an example solution with Date::Manip:
$input = "June 2006";
# these also work:
#$input = "2006 june";
#$input = "today";
#$input = "June 2006";
$thismonth = UnixDate($input, "%B %Y");
$lastofmonth = DateCalc($thismonth, "+1 month -1 day");
$dow_lastofmonth = UnixDate($lastofmonth, "%A\n");
This prints Friday
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