I defer to Physicist.
My meager understanding is that they don't. The gravitational field around a black hole is a "fossilized" remnant of the original star.
This begs the question: as a black hole sucks in more mass, it gets bigger and thus should have "more" gravity than prior to injestion of more mass. I suspect the answer is that the gravitation (gravitons, gravity waves) originate at the event horizon, not the geometric center of the hole.
Other than that, all I can say is that I have wondered about this question myself.
--Boris
Excellent question. If they have mass (do they?), presumably they can't escape. But obviously a black hole generates (so to speak) a lot of gravity, so ... as I said, an excellent question.
We need to be careful to distinguish between the gravitational field and gravitational waves.
The gravitational field is fixed to the black hole. In a nutshell, the gravitational field is the curvature of spacetime caused by the black hole. This curvature is defined everywhere in space, all the way up to the singularity at the center of the black hole; it is even defined inside the event horizon.
Gravitational waves are changes in the gravitational field. If a black hole is accelerated, obviously the field as it exists at some arbitrary point is going to change over time. This is perfectly analogous to the way electromagnetic waves are caused by the acceleration of electrical charges. If you move a charge around, the field associated with that charge will also be moved around. These changes in the field are propagated as a wave.
So in answer to your question, don't think of gravitational waves as radiating outward from a black hole like light from a bulb; rather, think of the gravitational field as being fixed to the black hole, with changes in the motion of the black hole thereby causing changes in the field.