Our Lady of Covadonga was open from 1915-1932 and was staffed initially by Jesuits. It was a Mexican/Spanish mission. The building that used to be Our Lady of Covadonga is a some kind of Christian Church now.
I did look for a cornerstone. No luck.
Pictures (taken March 11, 2010)
You can see some of the windows have been bricked up.
Cross up close
Crown in a window.
Looks Marian-ish to me.
I'm guessing this was the rectory.
It's attached to the church building.
Info from St. Louis Archdiocese Archives
Our Lady of Covadonga Info: here and picture of shrine