I have (okay, will have) an area just for special tree stumps so I can have a mushroom farm. Also, I like saying I have a "mushroom" farm.
I want to have every tree stump design in my town (just need clover, citrus & triforce). I have a few areas around my town that I want the stumps in, so I plant a tree, let it grow and then cut it down (2 strikes with gold axe and last strike with silver axe, 100% chance of getting special design). If it's a repeat design, I did it up and try again.
Silver axe, 100% chance of getting a special design. I have never had it fail. Just be sure to use the golden axe (or regular axe, if you don't have the golden one) for the first 2 strikes, then switch to the silver axe. This way your silver axe will last longer. I love the mushrooms that grow around them also. Will be using some for the Harvest Festivale when Franklin comes to town.
Every tree you cut down with a silver axe has a special stump?
Every single one.
If I find any, I'll keep them. The only one I got so far was destroyed by Agent S moving in. >_>