The Texas Local Government Code allows municipalities to appoint alternates as stated in Sec. 211.008 (c).
c) The governing body, by charter or ordinance, may provide for the appointment of alternate board members to serve in the absence of one or more regular members when requested to do so by the mayor or city manager. An alternate member serves for the same period as a regular member and is subject to removal in the same manner as a regular member. A vacancy among the alternate members is filled in the same manner as a vacancy among the regular members.
Due to the sporadic nature of the Zoning Board of Adjustment Meetings, it can sometimes be difficult to have a quorum. Appointing alternates would significantly reduce that difficulty.