The depolarization of the SA node relies on the funny current. The Funny channels are not singly-permeable channels - they are permeable to both K and Na (sometimes channels like these get called "Non-selective cation channels"). This is why the channel doesn't produce the kind of strong depol a pure sodium channel would produce or the hyperpolarization a pure K channel would produce - it produces a depolarization of intermediate slope, and since it is still a depolarization, you know its more permeable to Na than K. (
Wiki link)
Adenosine binds to A1 receptors, which are coupled to Gi and less cAMP. Less cAMP diminishes funny channel activity leading to an even flatter slow. It's activity also opens up more pure K+ channels (the ones that establish the RMP), which lead to a lower start point. These two combine to make Adenosine a negative chronotrope.
Adenosine acting on the AV node through the same receptor leads to less L-type calcium channel activity, and negative dromotrope effects.
Source:
http://www.cvpharmacology.com/antiarrhy/adenosine