Oysters are your best choice. Nameko is another one for willow. Lion's mane, chestnut mushrooms and comb tooth are rated as "satisfactory" on willow. Turkey tail is another one. Stumps should be freshly cut and free of any mold. This is best done in the early spring, but could be done now in colder climates where it rains in the summer.
There are two main methods. One is the totem method, here shown on logs, but you can modify this for stumps:
The other method is to drill holes in the stump then fill them with plugs. (Shown in the first part of this video):
Check out fieldforest.net for more info:
https://www.fieldforest.net/category/growing-mushrooms-on-logs
Field and Forest has the best selection of spawn and they are always super helpful. Good luck!