SET @date = NOW();
SET @date = '2010-02-01'; -- В таблице должно быть 4 строки
SET @date = '2017-10-01'; -- В таблице должно быть 6 строк
SET @firstDayNumber = (SELECT WEEKDAY(DATE_FORMAT(@date,'%Y-%m-01')));
SET @daysInMonth = (SELECT DAY(LAST_DAY(@date)));

SELECT
IF(id + 1 < 1 OR id + 1 > @daysInMonth, 0, id + 1) 'Пн',
IF(id + 2 < 1 OR id + 2 > @daysInMonth, 0, id + 2) 'Вт',
IF(id + 3 < 1 OR id + 3 > @daysInMonth, 0, id + 3) 'Ср',
IF(id + 4 < 1 OR id + 4 > @daysInMonth, 0, id + 4) 'Чт',
IF(id + 5 < 1 OR id + 5 > @daysInMonth, 0, id + 5) 'Пт',
IF(id + 6 < 1 OR id + 6 > @daysInMonth, 0, id + 6) 'Сб',
IF(id + 7 < 1 OR id + 7 > @daysInMonth, 0, id + 7) 'Вск'
FROM (
    SELECT 0 - @firstDayNumber id UNION
    SELECT 7 - @firstDayNumber UNION
    SELECT 14 - @firstDayNumber UNION
    SELECT 21 - @firstDayNumber UNION
    SELECT 28 - @firstDayNumber UNION
    SELECT 35 - @firstDayNumber
) AS t
HAVING NOT (Пн = 0 AND Вск = 0)