Isso funcionaria?
SELECT event_date, user
FROM eventlog
GROUP BY event_date, user
HAVING COUNT(*) > 1
ORDER BY event_date, user
O que está me atrapalhando é a cláusula COUNT(user) que você tem.
SELECT event_date, user
FROM eventlog
GROUP BY event_date, user
HAVING COUNT(*) > 1
ORDER BY event_date, user