Jane, you should make a habit of proving and documenting on your own all data posted to various sites. Because resources back when Arkansas was still a Territory of the US are few and far between, it sometimes takes a great deal of research into a wide assortment of sources - and a ton of time - to ferret out the facts.
We, at the Historic Genealogical Society, delve and dig long and deeply into every source we can find extant. We insist that our research be as accurate as is possible in spite of the scarcity of many records.
Some of the sources we have utilized in our research into the Coker/Trimble/Friend families include all 27 volumes of the Silas Turnbo manuscripts (familiarly known as Turnbo's Tales), "White River Chronicles of S C Turnbo" by Lynn Morrow 1994, "Reminiscent History of the Ozark Region" by Goodspeed 1894, assorted Knox Co TN records, assorted AR Territorial records, AR federal census records 1830-1920, area marriage records, area cemetery records, area land and tax records, the history of the creation of AR and its counties & attendant boundaries changes, and similar sources for TN, NC and MO records as well.
As for "proof" of the maternal parentage of Lucinda Coker, it's fairly simple. Much of that data cames from census records.
Lucinda m/1 Henry Nipps and their first child was born ca 1845. Therefore, Lucinda and Henry had to have been married at least 1 or 2 years before that. Hence, ca 1842. By the same token, Lucinda most likely would have been at least 18 when she married. Therefore, she would have been born ca 1824 (which fits nicely into the appropriate age slot in the 1830 and 1840 census records).
Lucinda's father, Charles Coker, was b in TN ca 1795-1800. He and his first wife, Elizabeth Trimble, were married in TN ca 1817. Elizabeth (Trimble) Coker d in Marion Co ca 1854. Therefore, somewhere between 1817 and 1854, they had Lucinda. As a matter of fact, they had 9 children between 1818 and 1843. It's possible that Elizabeth could have died before 1854, but she and Charley are very much alive in Marion Co in the 1850 census
Lucinda's father, Charles Coker, then a widower, m/2 ca 1854, Elizabeth "Betsy" Friend. They had 2 children - Charles M Coker b AR 1855 and Tilford D Coker b AR 1858. These children can be found in Stone Co MO in 1900.
No vital records were required in AR until Feb 1914. Before that date, the only requirement was for marriage records and these have always been maintained on a county level. The courthouse in Marion Co was burned to the ground at least twice during the Civil War (1861-1865) and again in August 1887. ALL records were destroyed.
Hope this clears up your problem. Oh, by the way. AR became a state in 1836. Before that date it was AR Territory. Until 1819 it was Missouri Terriotry. Marion Co was created out of Izard Co in 1836 and didn't exist as a county until statehood. And Elizabeth "Betsy" Friend is sometimes referred to as Cynthia "Betsy" Friend. You may run across this reference on some sites. We have found no basis for the given name Cynthia; therefore, we have chosen to use the references to the name Elizabeth, which fits more logically with the nickname Betsy.