  This is Part II of a two-part series regarding Ramsey properties of Fraisse
structures satisfying a property called SDAP+, which strengthens the Disjoint
Amalgamation Property. In Part I, we prove that every Fraisse structure in a
finite relational language with relation symbols of any finite arity satisfying
this property is indivisible. In Part II, we prove that every Fraisse structure
in a finite relational language with relation symbols of arity at most two
having this property has finite big Ramsey degrees which have a simple
characterization. It follows that any such Fraisse structure admits a big
Ramsey structure. Part II utilizes the notion of coding trees of 1-types
developed in Part I and a theorem from Part I which functions as a pigeonhole
principle for induction arguments in this paper. Our approach yields a direct
characterization of the degrees without appeal to the standard method of
"envelopes". This work offers a streamlined and unifying approach to Ramsey
theory on some seemingly disparate classes of Fraisse structures.
