Phylogenetic analyses of trait evolution can provide insight into the evolutionary processes that initiate and drive phenotypic diversification. However, recent phylogenomic studies have revealed extensive gene tree-species tree discordance, which can lead to incorrect inferences of trait evolution if only a single species tree is used for analysis. This phenomenon--dubbed 'hemiplasy'--is particularly important to consider during analyses of character evolution in rapidly radiating groups, where discordance is widespread. Here we generate whole-transcriptome data for a phylogenetic analysis of 14 species in the plant genus Jaltomata (the sister clade to Solanum), which has experienced rapid, recent trait evolution, including in fruit and nectar color, and flower size and shape. Consistent with other radiations, we find evidence for rampant gene tree discordance due to incomplete lineage sorting (ILS) and several introgression events among the well-supported subclades. Since both ILS and introgression increase the probability of hemiplasy, we perform several analyses that take discordance into account while identifying genes that might contribute to phenotypic evolution. Despite discordance, the history of fruit color evolution in Jaltomata can be inferred with high confidence, and we find evidence of de novo adaptive evolution at individual genes associated with fruit color variation. In contrast, hemiplasy appears to strongly affect inferences about floral character transitions in Jaltomata, and we identify candidate loci that could arise either from multiple lineage-specific substitutions or standing ancestral polymorphisms. Our analysis provides a generalizable example of how to manage discordance when identifying loci associated with trait evolution in a radiating lineage.