Their next fixtures features a trip to Skerries this weekend.
Tullamore got back to winning ways last Saturday in Division 2C of the AIL.
The Offaly club put up 35 points against Bangor, sealing the double against the County Down side.
That result leaves Tullamore second in the standings, with Instonians 13 points clear at the top.
A trip to play Skerries comes up this Saturday at 2.30.