Tullylish (In Antrim or Down?)

I believe one of my ancestors, Peter Devlin, was born in Tullylish in 1833.  I discovered his baptismal record using rootsireland.ie.

The baptismal record indicates the Tullylish parish/district is located in Co. Antrim - not Co. Down.

I have searched extensively for a Tullylish in Co. Antrim but continue to only find results for Tullylish in Down.  Is it possible the boundaries were different in the 1830s?

Any help or clafication would be most welcomed!

 

Thank you.