I have active rigid bodies on top of a passive rigid body. When I play the animation (no keyframes involved) the active rigid bodies start dancing around. See this GIF.
Firstly, you should ensure that you have Applied Scale to each of your objects (Ctrl+A, select Scale). Then, you can improve the accuracy of the simulation by increasing the Steps Per Second and/or the Solver Iterations settings on the Rigid Body World panel of the scene properties. See also Why my active rigid bodies are vibrating Continuously?