While it cannot be read in the above postcard, the distinctively-shaped sign out front of the tavern says "Cawley's" in this 1936 b&w photo, below
Here is the return address of a Cawley's envelope.
A 1936 advertisement
A 1930's black and white postcard photo of Cawley's. Part of the Cawley's sign can be seen. On the left side of the photo, the postmark has bled through from the opposite side of the postcard.