What features should a food processor have in order to make nut butters?
Resurrecting this thread in case people end up searching for it.  

The only requirement for which food processor is that the motor is powerful.  Underpowered will tax the motor too much. If the FP says that you can knead bread dough in it, it almost certainly will be fine.  Run long enough with a cutting blade, and you will get a smooth butter.

Blenders mainly have powerful enough motors, but they are not shaped properly to get thick/pasty substances in contact with the blades.  My Vitamix would work for a cup of nuts, but more would be too annoying.

Top end Breville FP that I have will make smooth nut butters, with the caveat that some nuts (hazelnut. Walnut) always feel somewhat “pasty” in comparison to peanuts or cashews.  I don’t add additional oil, so perhaps if I did so the mouth feel would be better.