@IsisRising08, from the archives, 12/16/1999 by James Binnion, Re: What to do with green tree stump:
"I got a green stump about 10 years
ago and had the same questions. What I was told was to paint the
cut ends of the wood with linseed oil every few weeks to reduce
the rate of drying out. If you do not do this it will crack and
become useless. If the the bark starts to come loose and expose
the wood on the side of the trunk then paint those areas with
linseed oil as well. This worked well for me my stump only had
minor cracks and dried out in about a year."
Be aware that linseed oil (on rags, brushes) can spontaneously combust, so you need to save or dispose of them in a safe way. As the linseed oil oxidizes it gives off heat, and you don't want that heat 'contained' so it keeps building up until it is hot enough to ignite.
The following is from http://www.finewoodworking.com/2009/05/08/how-to-safely-and-not-so-safely-dispose-of-oil-soaked-rags
"[The solution] “...requires either destruction by something like burning, or a safe way to let the material cure without cumulating heat. For home and small commercial shops, the easiest way is to spread the rags in a single layer [such as on a trash can lid] so heat dissipates while the material cures. Then, depending on local regulations, the materials can be safely disposed of, either in hazardous waste collection sites, or in the general landfill.”