Several recently proposed program logics have incorporated notions of \emph{underapproximation} into their design, enabling them to reason about reachability rather than safety. In this paper, we explore how similar ideas can be integrated into an expressive type and effect system. We use the resulting underapproximate type specifications to guide the synthesis of test generators that probe the behavior of effectful black-box systems. A key novelty of our type language is its ability to capture underapproximate behaviors of \emph{effectful} operations using symbolic traces that expose latent data and control dependencies, constraints that must be preserved by the test sequences the generator outputs. We implement this approach in a tool called \name{}, and evaluate it on a diverse range of applications by integrating \name{}'s synthesized generators into property-based testing frameworks like QCheck and model-checking tools like P. In both settings, the generators synthesized by \name{} are significantly more effective than the default testing strategy, and are competitive with state-of-the-art, handwritten solutions.