S.D. Codified Laws § 15-9-7
A summons, writ, order, or decree may be served by publication under the conditions and in the manner provided hereinafter and in §§ 15-9-8 to 15-9-21, inclusive.
Where the person on whom the service of the summons, writ, order, or decree is to be made cannot, after due diligence, be found within the state and that fact appears by affidavit to the satisfaction of the court or a judge thereof, and it in like manner appears that a cause of action exists against the defendant in respect to whom the service is to be made or that he is a proper party to an action relating to real or personal property in this state, or to the writ, order, or decree, such court or judge may grant an order that the service be made by publication of the summons in any of the cases described in §§ 15-9-8 to 15-9-15, inclusive.
SDCL 15-9-7