Can a dependent current or voltage source make a circuit unstable?
Yes, absolutely it can make a circuit unstable.  

A voltage controlled voltage source is nothing more than a gain block, and if you have other circuit elements that cause the open loop phase to be greater than -180 degrees when the open loop gain crosses 0dB you have an oscillator when you close the loop.

Same goes for other dependent sources with appropriate circuit elements.

So you can easily make an unstable circuit with a dependent source, but there's no reason you can't design a stable circuit as well.