Tex. R. Civ. P. 635
At any time within ten days after the rendition of any judgment in a justice court, the justice may grant a stay of execution thereof for three months from the date of such judgment, if the person against whom such judgment was rendered shall, with one or more good and sufficient sureties, to be approved by the justice, appear before him and acknowledge themselves and each of them bound to the successful party in such judgment for the full amount thereof, with interest and costs, which acknowledgment shall be entered in writing on the docket, and signed by the persons binding themselves as sureties; provided, no such stay of execution shall be granted unless the party applying therefor shall first file an affidavit with the justice that he has not the money with which to pay such judgment, and that the enforcement of same by execution prior to three months would be a hardship upon him and would cause a sacrifice of his property which would not likely be caused should said execution be stayed. Such acknowledgment shall be entered by the justice on his docket and shall constitute a judgment against the defendant and such sureties, upon which execution shall issue in case the same is not paid on or before the expiration of such day.
Tex. R. Civ. P. 635