I think that this will work for you:
SELECT temp_date,
COUNT(*)
FROM (
SELECT ((SELECT MAX(date_start) FROM {dates_table}) - INTERVAL c.number DAY) AS temp_date
FROM (SELECT singles + tens + hundreds number
FROM ( SELECT 0 singles
UNION ALL SELECT 1 UNION ALL SELECT 2 UNION ALL SELECT 3
UNION ALL SELECT 4 UNION ALL SELECT 5 UNION ALL SELECT 6
UNION ALL SELECT 7 UNION ALL SELECT 8 UNION ALL SELECT 9
) singles
JOIN (SELECT 0 tens
UNION ALL SELECT 10 UNION ALL SELECT 20 UNION ALL SELECT 30
UNION ALL SELECT 40 UNION ALL SELECT 50 UNION ALL SELECT 60
UNION ALL SELECT 70 UNION ALL SELECT 80 UNION ALL SELECT 90
) tens
JOIN (SELECT 0 hundreds
UNION ALL SELECT 100 UNION ALL SELECT 200 UNION ALL SELECT 300
UNION ALL SELECT 400 UNION ALL SELECT 500 UNION ALL SELECT 600
UNION ALL SELECT 700 UNION ALL SELECT 800 UNION ALL SELECT 900
) hundreds
ORDER BY number DESC) c
WHERE c.number BETWEEN 0 AND (SELECT DATEDIFF(MAX(date_end),MIN(date_start)) FROM {dates_table})
) calendar
JOIN {dates_table} ON temp_date BETWEEN end_date AND start_date
GROUP BY temp_date
Just replace {dates_table}
with the name of your table.
The base of this that generates the series of dates was taken from IvanD's answer on this SO question: How to populate a table with a range of dates?