The .270 will do the job with a bonded or TSX bullet, but it should be considered minimum and treated as such.
Here's the most important part on hunting Nilgai:
-Shot placement! Study their anatomy and either put that bullet low and forward, or take out the spine. You are trying to bust up the shoulder and take out the heart, or sever the spine (I prefer the heart). A lung-shot bull can go a long way in some nasty brush, and the spine doesn't have a high margin of error.
-Keep shooting until he's down! If I had a dollar for every hunter who put 1 shot in a Nilgai then pulled out of the scope and watched it run off I'd be able to buy something nice. Stay in the scope, jack another round in the chamber, and don't stop until he's down for good.
FYI: Nilgai are famous for going down at the first shot, but then struggling up and running off. Stay in the scope until you're sure. The bull in my sig took 225 gr through the heart from my .338 Win Mag and STILL tried to struggle to his feet. Tough critters.
When is your hunt? You going to Laguna Atascosa? Good luck to ya, and keep us posted!