During its short life, it had two capitals: first Saltillo, and then Monclova (the dispute between the two rivals is dealt with in greater depth at the latter city's article).
For administrative purposes, the state was divided into three districts: Bexar (the entire area covered by Tejas), Monclova (northern Coahuila), and Río Grande Saltillo (southern Coahuila).
It remained in existence until the adoption of the 1835 "Constitutional Bases", whereby the federal republic was converted into a centralised one, and the nation's states (estados) were turned into departments (departamentos): the State of Coahuila y Tejas was split in two and became the Department of Coahuila and the Department of Tejas. The latter would, of course, later become the Republic of Texas.
Compendium of Mexican Constitutions (http://www.cervantesvirtual.com/portal/constituciones/pais.formato?pais=Mexico&indice=constituciones) (in Spanish)
A provisional chief was appointed for Texas in August 1824, and in December the Department of Texas was legally established as a subdivision of the state of Coahuila and Texas.
Viesca and the remaining members of the legislature were arrested in Coahuila.
The severance of Texas and Coahuila was made final by the Texas Revolution and the Mexican War.