I think all the info we are given on the Beornlings is that they lived in the lands between Mirkwood and the Misty Mountains, and after the events of TH, they started taxing the road from Mirwood that ran over the Carrok to the Misty Mountains. As such, I think it may depend on when you want you army based.
Prior to TH/just after, I'd go for a 'poor' colour scheme - i.e. browns and off whites. Paint the tunic, trousers and cloak with Denheb Stone and then wash the trousers with Ogryn Flesh and the cloack with Devlan Mud and slighty highlight the tunic. Paint the leather and skin as you would normally, and the hair brown or black. Swap around the position of the three clothing colours to add variety while retaining uniformity.
Post TH, you could use red, blue and or green instead of the browns, and highlight the off white areas with more white to represent them using their increased wealth to import dyes and higher quality clothing.