You could take a look at Cones and duality by Aliprantis and Tourky. Specifically Sections 1.6 and 1.7 may have some results that could be of interest to you. Google Books

The authors define a notion of basis of a cone (a set $B$ in the cone so that every vector in the cone is a positive real multiple of an element in $B$; think unit sphere intersected with the cone), but I wonder whether that is what you have in mind. If you mean that every vector in the cone can be written uniquely as a positive linear combination of (extremal) vectors in the cone, then you might want to take a closer look at what are called lattice cones (in finite dimensional spaces, or equivalently, finite dimensional Riesz spaces). Introduction to operator theory in Riesz spaces by Zaanen gives a very gentle introduction to the subject (so don't let the term "operator theory" scare you off). Google Books