It has been my experience that I can, most of the time, find the really old obituaries by contacting the library or archives and ordering them. However, finding the ones that are either recent or not really that old- sometimes proves not that easy. Below are some links that I have found quite useful in obtaining obituaries. Many of these are from areas outside of Morgan County, but I have consistently found my ancestors obituaries in these areas. If when reading obituaries, you look near the end, you will find the mention of the funeral home and sometimes a link to it.
I should note that on some of these links, you may have to scroll to the bottom of the pages to obtain the links for the Obituary Archives.
If anyone should have any other sources, please send them to email@example.com