The Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) is a prolific muon producer, making it an ideal location for studying dark sector particles produced in muon decays at rest. In this paper, we explore sub-GeV dark particle detection possibilities in a tons-scale, highly capable hydrocarbon scintillator (HC${}^2$) detector at the SNS. We consider a search for $e^{+}{e}^{-}$ final states produced by decays of long-lived, $𝒪(10-100)$~MeV axion-like particles and heavy neutral leptons. The HC${}^2$ technology space, exemplified by the PROSPECT and Mobile Antineutrino Demonstrator detectors, offers strong rejection capabilities for the cosmic ray backgrounds that would normally dominate this search. By benchmarking on-surface cosmic ray signatures with data from PROSPECT at ORNL, we generate robust predictions for a multi-year SNS deployment of a range of HC${}^2$ detector implementations. Results indicate the potential for order-of-magnitude improvements in sensitivity to axion-like particles and heavy neutral leptons in the 10-100 MeV mass regime compared to current global limits. We also comment on the neutrino detection possibilities of a HC${}^2$ deployment at the SNS.