I'm unable to find any song with that exact title, or containing those exact lyrics "I'll never see those blue eyes again" – by Ernest Stoneman or anyone else.

The closest I've gotten are these:

A. P. Carter's I'M THINKING TONIGHT OF MY BLUE EYES

Johnny Cash's I STILL MISS SOMEONE contains the line "I never got over those blue eyes"

BEAUTIFUL BROWN EYES contains the line "I'll never love blue eyes again"