We show that engineered photonic metamaterials composed of alternating layers of suitable dielectrics and metals can support different kinds of surface waves (SWs) under robust and readily achievable experimental conditions. The supported SWs include Dyakonov SWs, hybrid plasmons, and Dyakonov plasmons. In particular, in contrast to conventional physical settings, we show that the high form birefringence exhibited by the metamaterials allows Dyakonov SWs, or dyakonons, to exist within large angular existence domains and levels of localization similar to plasmons, thus making dyakonons available for practical applications.