Or between ammonia and aluminium trichloride; I have a choice between the two. It's the last question in my assignment : )
I am thinking maybe dative covalent/co-ordinate bonding between the two lone electrons on the nitrogen of the ammonia ion and the boron of the BCl3?

Yes, it's possible.

It cannot be permanent dipole dipole because boron/aluminium trichloride is not polar.