New Mexico Territorial Laws and Treaties NM TERR LAWS KEARNY CODE CT & J POWERS § 11

Upon the appeal being made, the circuit court shall make an order allowing the same, such allowance shall stay the execution in the following cases and no others:

A. when the appellant shall be executor or administrator, and the action by or against him as such;

B. when the appellant, or some responsible person for him, together with two sufficient securities, to be approved by the court, during same time at which the judgment or decision appealed from was rendered, enter into a recognizance to the adverse party in a sum sufficient to secure the debt, damages and costs recovered by such judgment or decision, together with the interest that may grow thereon, and the costs and damages which may be recovered in the superior court, conditioned that the appellant shall prosecute his appeal with due diligence to a decision in the superior court, and that if the judgment or decision appealed from be affirmed, or the appeal dismissed, that he will perform the judgment of the circuit court, and that he will also pay the costs and damages that may be adjudged against him upon his appeal.