We propose an acoustic metasurface for perfect absorption at dual frequencies within a compact space. Meta-molecules of the metasurface contain four subwavelength meta-atoms whose cavities are coiled by three foldings. The meta-atoms comprising a meta-molecule have slightly different neck sizes to obtain hybrid resonances at desired frequencies. In order to consider an effect of coiled spaces in the meta-atoms, we use equivalent straight cavities with an effective length in an analytical model. By using the analytical model, metasurfaces are optimally designed for perfect absorption at desired frequencies. The experimental results show that a lambda/23-metasurface exhibits over 99% energy absorption at 294 Hz and 406 Hz. Furthermore, we define another optimization problem to minimize the thickness of the metasurface for perfect absorption at two desired frequencies. The experimental results show that a lambda/32-metasurface exhibits over 91% energy absorption at 281 Hz and 99% sound energy absorption at 403 Hz. Published by AIP Publishing.