I know there have been a number of threads involving this talk, but hear me out! With the blood of angels book, there are a number of variations to the aasimar, one of which is Agathion-Blooded Aasimar. This particular race has the following trait available.
Enlightened Warrior:You have always found it easy to maintain inner peace and enlightenment that translate well to the battlefield. You may take levels in monk even while maintaining a neutral or neutral good alignment.
In theory this means that one can be both a monk and a barbarian at the same time, though the problem is that the only stats that help this build, that the Agathion-Blooded Aasimar has is +2 con, the char may be benificial for barbarian things, however from a defensive stand point it is useless as memory serves
Or you could get into intimidating to use that +2 Cha. There's relevant rage powers, and a scaled fist or nornkith monk can use Cha instead of Wis.
That's one of the 4 ways I remember to combine those two classes (not counting 'just play a bloodrager'). The martial artist monk archetype and menhir guardian monk, and the geminate invoker barbarian all alter their classes alignment restrictions in ways useful to this. Edit: a quick check tells me that there's another way now, the elemental monk, and the karmic monk has existed for a while though I hadn't previously noticed it.