Sublimation will only work on synthetic materials. So unless the felt is man made from a poly based material, that process will not work. If you were able to print the correct placement before the felt is applied to the table then you could have it printed directly. Another post install option that would work well would be a transfer material that could be heat applied. Here's an example of one that would work:
http://www.thepaperranch.com/shopexd.asp?id=757 , that is a product that I have used in the past on a vast array of natural materials and the durability is great. Do you know if the artwork is a single color? If so, there are many colored vinyls that would work great as well.
www.specialtymaterials.com is a great place to start when looking for heat applied vinyls.
I spent 4 years in the garment decoration industry as a equipment and materials distributor and technical support specialist. I figured I would add that info so you didn't think I was repeating some info that I found online.