Check the weather with the Karnataka government on their website on the heavy rains in Coorg. Mysore is lovely, crowds will start picking up as we will be heading to Dussehra ;)
Post monsoon (after September) is one of the best season to visit hill stations in South India. Do carry some warm clothes as the weather will be pleasant. There is a long weekend coming up in October 1st week. You may find some crowd as well.
Coorg bears a tropical weather making it an ideal holiday destination, throughout the year the climate remains pleasant to visit. However, the best time to visit is from the month of October to May.
Mysore surely has a tropical climate, but the Monsoons and Winter are the best time to visit the city. The monsoon - winter months from July - February has pleasant weather as a respite from the intense heat of summer.