How to prevent tofu from falling apart on the grill?
Standard tips for browning/frying/grilling tofu;


Ensure that you press the tofu sufficiently to remove its own moisture, marinate if desired
Lightly dust with flour
Brush oil on the grilling surface


The same advice applies for pan frying. I prefer to work at a high temperature, others have had very good results using only medium. Use a very thin, flat metal spatula to turn. Specific to the case of grilling, be mindful of the gap the tofu will stretch across on the grate; it may be crumbling because it isn't strong enough or thick enough to sustain wide gaps.

Additionally you can pre-bake the tofu to dry it out further. I have heard tell that salting lightly with finely ground sea salt helps prevent sticking but have no experience with this, and have had good results without the added sodium.

Typically the moisture in the surface of the bean curd is causing the sticking. Prevent or inhibit this and you should be good.