I drink coffee during IF and have no problems. Here's from Mark Sission's FAQ:
Can I drink coffee or tea during a fast? How about adding cream or coconut oil to it – will that take me out of the fasted state?
Coffee is actually beneficial for fat-burning, especially during a fast. One study found that an infusion of epinephrine – a hormone which coffee increases – during “starvation” enhanced its lipolytic and thermogenic effects. In other words, fat-burning and metabolism up-regulated in response to epinephrine (more so than usual). Epinephrine also lowers appetite, which can be extremely helpful for people trying to stave off hunger during a fast. Tea, and anything non-caloric, is also fine.
Adding a pure fat source won’t “take you out” of the fasted state, and it may take the edge off the hunger, but it will reduce the body fat you burn by a bit.
Read more: http://www.marksdailyapple.com/fasting-questions-answers/#ixzz21ZL8ULyx