In the 1930 Federal census, Ernest E Coulter (26y) is listed with his wife Mary (18y) and their baby daughter Ernestine, living in Jefferson, Cole, Missouri. It lists both of his parents, as well as both of Mary's parents, as being born in Missouri.

On the SSDI, he is listed as Ernest Colter (without the "u") ...

I haven't been able to locate him on the 1910 or 1920 census records ... His name was probably misspelled or abbreviated in some way. I've found people I was looking for indexed under names that were far different than what the census (and family records) showed them as being. Finding Ernest is not impossible, but it will probably be a challenge. But I'm sure you will do it!

Best of luck ... I wish I was able to help more.
KTaylor