Hand, foot and mouth disease (HFMD) is a serious public health problem, and coxsackievirus A6 (CVA6) and coxsackievirus A10 (CVA10) are two of the major causative pathogens, in addition to enterovirus 71 (EV71) and coxsackievirus A16 (CVA16). A simple and rapid reverse transcription recombinase-aided amplification assay (RT-RAA) was developed for the detection of CVA10 and CVA6 in this study. The analytical sensitivity for detection of CVA10 and CVA6 at 95% probability by probit regression analysis was 35 copies per reaction and 38 copies per reaction, respectively, with 100% specificity. Compared with commercial RT-qPCR assays, when testing 455 fecal specimens, the kappa value of the RT-RAA assay for CVA10 and CVA6 was 0.920 (p < 0.001) and 0.952 (p < 0.001), respectively. Moreover, four samples that were positive for CVA10 and five that were positive for CVA6 by RT-RAA but negative by RT-qPCR were further determined to be true positives. These results demonstrate that the proposed RT-RAA assays are very valuable tools for the detection of CVA10 and CVA6 and have potential for use in resource-limited settings.