$sth = $dbh->prepare("select count(*) from table_one");
$sth->execute();
$row1 = $sth->fetchrow_array;
$sth = $dbh->prepare("select count(*) from table_two");
$sth->execute();
$row2 = $sth->fetchrow_array;
Unrelated comment: with DBIx::Simple, you can save yourself some typing.
$db->query('select count(*) from table_one')->into($row1);
$db->query('select count(*) from table_two')->into($row2);
or even, giving up a lot of speed:
$db->select(table_one => '*')->into($row1);
$db->select(table_two => '*')->into($row2);
DBIx::Simple caches queries automatically, so there is no need to separate prepare and execute yourself.