We propose a thermodynamically consistent symbolic-regression framework to discover convex dual dissipation potentials for viscoelastic materials directly from stress-strain time series. Starting from the Clausius-Duhem inequality within the generalized standard materials setting, we express the internal-variable evolution as a gradient flow driven by the thermodynamic force through a dual dissipation potential. The learning task is thus recast as identifying an explicit, parsimonious expression for the dissipation potential whose convexity guarantees non-negative dissipation and well-posed evolution. A central contribution is a convexity-preserving grammar that embeds thermodynamic admissibility into the hypothesis space. Candidate expressions are generated by rules that ensure closure under positive linear combinations, employ convex primitives, and restrict function composition to preserve convexity throughout the expression tree. Genetic programming explores this constrained space, while an embedded parameter-fitting stage calibrates coefficients for each candidate structure by minimizing stress reconstruction error under time rollout of the internal-variable evolution equations. We assess the approach on synthetic "virtual DMA" datasets generated from a one-dimensional generalized Maxwell solid spanning multiple strain amplitudes and frequencies, with both additive measurement noise and temporally correlated (Ornstein-Uhlenbeck) perturbations. For a Newtonian-viscosity ground truth, the exact quadratic structure is consistently recovered with low prediction error. For a nonlinear power-law dissipation, the dominant identified form matches the underlying power-law behavior across nearly all realizations, again with small test errors. The framework is further validated on experimental DMA measurements, demonstrating that the identified potentials accurately reproduce the measured storage and loss moduli across multiple strain amplitudes and frequencies. Overall, the proposed convexity-preserving symbolic framework provides an accurate, interpretable, and thermodynamically consistent route for data-driven identification of dissipation mechanisms in viscoelastic materials.