There is no record of two priests dying in Texas during the Civil War. However, two Spanish missionaries, Fathers José Francisco de Escamilla and Juan de Zuniga, were killed in the 1758 raid on the San Xavier missions by Comanche, according to 

Texas Monthly. One notable priest death during the 19th century in Texas was Father Michael “Mickey” McEniry, who died in 1839 during the Texas Revolution. 

• 1758 San Xavier Mission Raid: In the 1758 raid, which was not during the Civil War, but rather during the Spanish colonial era, Fathers José Francisco de Escamilla and Juan de Zuniga were killed along with six other Spaniards.
• 1839 Texas Revolution: Father Michael “Mickey” McEniry, an Irish priest, was killed in 1839 during the Texas Revolution when he was traveling between missions in Texas and Mexico. 

A separate event occurred in 1758 in Texas, where the Apache and Comanche tribes were in conflict. Spanish missionaries were killed during this period, but this was not during the Civil War. 

Ghosts Of War – Texas Monthly

Mar 5, 2017 — As massacres go, the body count at the mission was fairly modest. A mounted horde of two thousand Comanche and their allies burned the mission on Mar…

Texas Monthly

Martyrs of the Spanish Civil War – Wikipedia

During the Spanish Civil War of 1936–