Monocle! Mr. Peanut wears a monocle.
For everyone who must be doing a crossword puzzle and needs the name for "Mr. Peanut's Eyewear," and who is Googling that phrase, which then brings them to my blog (where I mention Mr. Peanut AND eyewear)...
The word is MONOCLE.
Does it fit?
EDITED TO ADD: Yes indeedy! Today in the Boston Globe crossword puzzle, which must be a syndicated puzzle, there it is: 21 across--Mr. Peanut's eyewear