Wyo. Stat. § 1-21-511: Right to stay of execution.

Except as otherwise provided, any person against whom judgment is rendered may have stay of execution by entering into a bond with the adverse party within ten (10) days after rendition of the judgment, with good and sufficient surety, resident property holders of the county, approved by the judge, conditioned on the payment of the amount of the judgment, interest and costs that may accrue. The bond shall be entered on the docket and signed by the surety.