S.D. Codified Laws § 21-49-16

If the defendant is a nonresident of the state, or absent or concealed, or if he is a resident of the state and after due diligence cannot be found in the state, service may be made by publication in the manner prescribed by statute or rule of court in ordinary civil actions. If any proper party defendant is deceased, service upon unknown heirs, devisees, legatees, personal representatives, creditors, and other unknown persons who might have a right of redemption from the mortgage, may be made by publication, as provided by § 15-9-9.