Charlie would have been about 76 years old in 1936 when they started social security, so he probably never applied, and therefore no accurate death record exists from this source for him.
But to search for a marriage record for him and Millie would mean getting any old records, like birth certificates from the older family members or family bibles with the record years recorded inside.
The year of birth of the oldest child they had, did you say his name was William, followed by Merle, followed by Cora; this year would tell us how to guess the year of marriage within five years.I searched Illinois database adn came up with nothing, but maybe they were married in Missouri, and not in Illinois.I do not know how to find a record that old in Missouri, but there must be someone who can help.The normal procedure is to locate the city or the county they lived in and send for a search from the county recorder office; they do keep old county records, if there was no fire or flood to harm them.So the records might still be there.And sometimes the records do contain the names of the parents of the bride and groom.So you need to locate a place they lived inMissouri and search the records of that place, it seems.
Also, go towww.familysearch.organd find out which of the 1880 census records is your Charles Harris, and use this information to help out with your further searching.You will have to think carefully and make some decisions and choices.
Others here may have access to more census years, but you will need to provide a time span that they lived in particular places in Missouri, in order to find out Millie's age and place of birth from a census record.
There is a Millicent Harris 1880 Census record for someone about the same year of birth as Charles,that was very interesting to read, but it is unusual for two people of the same surname to marry.It does happen, though.