I am not sure and am only a layperson on this (math grad school, physics undergrad) - conceptually you could think of a blue giant orbiting at 0.99c, but
a) the orbit would be so large that the actual acceleration is fairly small, or
b) the centripetal forces of a small, relativistic orbit would rip the star into pieces. In particular this would dramatically reduce the effective density of the accelerating mass.
Having enough gravitational force to retain coherent structure while accelerating quickly enough to generate gravitational waves seems like a tough circle to square.