Sure you can query database state and filter out the unwanted:
select name, state_desc
where not state_desc in ('Offline', 'Recovering')
The SCOM Monitor "Database Status" from MSSQL on Windows Management Pack checks if a DB is in offline, recovery, suspect or emergency state. But I can't configure, that it only alerts, when the state is suspect or emergency. Offline and Recovery are not a bad state for me, so i don't wanna an alert.
Is there a way to create my own monitor, that only alerts when the state is offline or emergency? Maybe with the SQL Query SELECT name, state_desc FROM sys.databases?