Dromore Down, Dromore Tyrone

Two compeletely different towns and parishes, in different counties. They just share the same name (as many towns and parishes do in Ireland).

So I am correct in assuming a Banbridge registration would be in Dromore Down?

If you want to see what towns or townlands are in a given registration area use this site below. (Search under Poor Law Union as the boundaries for most PLUs are also the civil registration district boundaries).

http://www.thecore.com/seanruad/

Parishes have different boundaries and can often be split across several registration districts.

Your question is where would a registration in Banbridge be registered. The answer is Banbridge.  Dromore isn’t a civil registration town, it’s a parish and a small town. Some townlands in Dromore have Banbridge as their civil registration district. Others have Lisburn. The seanruad site above tells you precisely which.