6-14-22 thanks to James (47839669) for Suggested edit:
I am making this edit due as there is no evidence Lucinda's daughter Sarah was daughter of this particular Martin Cooper. I don't believe Martin ever lived in or near Perry County. There is also no evidence this Martin was ever married to Lucinda Taylor. If he was, something was seriously wrong because at the time Lucinda and [likely a completely different] Martin Cooper married, this Martin was still married to his wife Minervia McCormick.

7-14-22 thanks to Searching for Answers (46881808) additional info:
The above appears incorrect on the point that Martin's wife Minervia, whom he reports Martin was still married to during the time Sarah was born, was not married to Minervia at that time. It appears they were divorced before 1842 and Minervia remarried another man in 1842 named Harkrider. See memorial for Minervia (McCormick) Cooper-Harkrider.

4-20-23 thanks James (47839669) for additional info:
Lucinda and Martin married in February 1839 in Perry County. This was over 3 years before Martin Cooper and Minerva McCormick of Hendricks County (150 miles away) divorced in April 1842. (They had married in 1836). This alone should serve as an alert that we are probably dealing with two completely different Martin Cooper who happened to share the same name.

To add to this, there appears to have been only one Cooper household in Perry County in 1840. This was James Morgan Cooper who married Sarah Lamb in Perry County December 1839. On the 1840 census, this James Cooper is residing only a few households from Nancy Taylor, Lucinda Taylor's mother, and appear on the same page.

It appears James Cooper came to Perry County, from Kentucky, with a few brothers. One brother was William buried in Gibson County (although his first wife was buried in Perry County). Many family charts on Ancestry indicate James and William were sons of William Cooper and Elizabeth Gilmor, of Breckinridge County, KY. If one looks at family charts for William and Elizabeth, a number of them indicate they also had a son named Martin. This Martin was almost certainly the person who married Lucinda Taylor. It's unknown what became of Martin. If I were to guess, he died within a short time of Sarah Cooper Beard's birth.

The evidence that a sibling of James and William Cooper named Martin married Lucinda Taylor appears to be pretty strong, and the evidence that Martin Cooper of Hendricks County, IN, married Lucinda Taylor simply does not exist.