We get a fair number of genealogy questions from people looking for information on their methodist ancestors. 9 times out the more appropriate resources for their questions are the local church where their ancestors served. If the the church was closed, the records go to the new church, if that church closes the records go to the conference archives.
The General Commision on Archives and History, The United Methodist Church has a really great guide to locating ordained ministers. The guide walks you through the questions you'd need to ask you do genealogical research. Often the answer is "contact your conference archivist".
So how can the Divinity School Library help you? If your ancestor was an ordained minister in a North Carolina Church, you may be able to find them in the conference memoirs index (left hand isde of the General Commission on Archives and History research page). The index lets you search by first name, last name and provides a page reference to the conference and page number the obituary appears in.
The Divinity School Library has the North Carolina Conference journals and will be able to locate the obituary. Many of these conference journals are available online in the Internet Archive. The Religion in North Carolina Digital Collection is also a great rsource for records of ordained clergy in North Carolina from a number of denominations. Unfortunately, most genealogy questions (unless they were for a NC methodist preacher) couldn't be answered by any of the resources that we have at the Divinity School.