ULQ2003 not driving a Relay properly
The issue here is that you have COM connected to 9V. 
If you look at the internals of the ULQ2003, you will see that between its output and COM there is a diode, the same diode that you have added in parallel to the coil of the relay.

Because of this, when you try turn the output of the ULQ2003 off, effectively you will still have 3V going through the coil of the relay, which is enough to keep it energised