At the outset of the WOT5K, why did neither of the Baratheon brothers try to approach the Stark/Tully coalition? It seems as though the entire southern continent was making deals with each other, but no one thought to get the North on their side?

I think you have to keep in mind the timing and sequence of events: Renly had just crowned himself (after screwing up his pitch to Ned) when Robb Stark was acclaimed king, and Stannis had yet to release his public letter, let alone ask anyone beyond the Stormlands for support. 

But despite that, Catelyn does go to Bitterbridge to negotiate with Renly and talks to Stannis as well.