BBQ Beef Brisket on a Propane Grill?
You can get extremely edible results, which is good enough for me.  The smoke-ring may be lacking from a competition grade result, but the flavour will be fine.

Presume you have a big-enough BBQ to have at least two burners.  Only use the burner the meat is not on.  If you have any prevailing wind and are not completely sheltered, make the hot side the upwind side.

Either get a smoke-box, or do what I used to and use foil.  Soak 1/3 to 1/2 your wood chips in water to slow them down.  Foil worked just fine for me, made a pouch, put in the chips and poked the up-flat-side with a knife to make smoke holes.

If you have a larger BBQ, consider adding in bricks or stones (no river stone!) to help maintain even heat.  By having less air and more thermal mass, you will do better.

Let me meat come to room temperature before you put it on.  Also no need to smoke right away, as the meat will not take it until it heats up further in the BBQ.

Happy Eating