Unfortunately its pretty tough to identify what youre dealing with based on that info. It would be easy to say coyote, but i would think you would have heard some, and i cant see a yote leaving behind these remains. Otherwise youre looking at any number of predators. But, If i had to guess...
My best guess would be feral cat. They are stealthy, they dont mind being near houses, and they are rabbit killing machines. The fact that some remains were left behind makes me think it was a smaller predator. Good luck.