By Goedels completeness theorem satisfiability in first-order logic is $\Pi_1$. So to obtain decidability in some fragment, it is enough to show that satisfiability is $\Sigma_1$ in this fragment. I wonder if the following technique can work.
Let $\cal F$ be a set of first-order formulas and $\cal M$ a countable set of structures. Assume we can prove that if a sentence $\phi \in \cal F$ is satisfiable, than it has a model $M \in \cal M$. Assume further that $M \models \phi$ is decidable (or at least semi-decidable). Then the satisfiability for $\cal F$ will be $\Sigma_1$ and hence decidable.
Does anybody know results along these lines?