While I was at the Toledo-Lucas County Public Library Friday looking up some other information, I checked the "Lucas County Birth Index" for a male Cooper born ca 1868. Knowing that marriages were first recorded in Ohio in 1835 and births and deaths in 1867, John's son should be in the earliest volumes. Listed was Cooper, son of John Nov. 2, 1867 in volume 1, page 8.
These records are not the originals but are microfilmed copies. I and a librarian tried multiple times to get a legible copy, to no avail. Only legible were the first few words, Cooper son of John. Even the column headings were illegible but presumably they are Surname, Given Name.
The index was typewritten, confirming that it was prepared using the original records. Perhaps a copy of the original record from the Probate Court would be clearer and more legible than a copy.
In past years I have obtained copies of birth and death records for folks like you but for various reasons it is just not an option now. On-street parking is basically zero and parking in a lot is very expensive, staff has been reduced to the very minimum even though the demand for certified information is still very much in demand, the cost of copies has increased five-fold from $1 a few years ago, etc. On the flip side, if you order a copy, your only expense is $5 with minimal time involved and you have the copy in your possession. As you know, documentation is extremely important.
I appreciate your kind words. I still venture to the library at least monthly looking up information for out-of-state seekers. I know it is difficult for folks to find needed information when they live hundreds of miles away and don't want or can't afford to pay $40+ an hour to a certified genealogist.
As for my genealogy it is partially done with documented information on my maternal side back to 1711 in Germany. But until I hit the mega-bucks lottery or a rich relative leaves me a bundle, it is done. Neither option will occur.