Now onto the subject concerned in the original post.
You can force graft most corals. It is just not remotely easy. I have personally successfully grafted two montiporas together, however I lost my grafted result

out:, via a method I learned from an ex-sps addict who successfully grafted SPS this way. SPS
seem to be the easiest to graft. I am not 100% sure why, but I would assume it is has something to do with them having a thin amount tissue on their skeleton, a great amount of polyps per colony, the fact that they consume mass amounts of particulate matter, a mixture of those, or something similar. Those characteristics seem to supply the most reason for more easily transmitted pigments in my opinion. Both natural and force grafts of SPS have been and are continuing to be seen in the hobby.
On to LPS! Grafted LPS they do exists. WWC sold an amazing grafted australomussa a few months ago and Cornbred has a grafted chalice that consists of Bubble Gum Monster and Miami Hurricane in his collection. I do not know much about force grafting LPS, so I will not include potentially false information in the post to save you all a headache or two.
Opinion--> I personally believe grafted LPS occur more often than the hobby thinks, but we do not want to accept it because then grafted LPS would not be as fun. I developed that belief from seeing the Widowmaker chalice, its hundreds of look alikes, all of these rainbow chalices recently, in addition to bi-color single polyped LPS, and a few others.
<--Opinion
Now the softies! I think soft corals graft the easiest out of all of our common corals but I also think they lose their graft the easiest because they can deflate and inflate so easily via transfer of liquid internally to externally and the other way around. A few polyps have been successfully force grafted in the past, for example the two-face protopaly that mixes the Nuclear Green Protopaly with the Purple Death Protopaly. I also think I remember this graft naturally occurring in someones tank via juxtaposition of two colonies, but do not hold me to that statement. To date the only successful force grafts that I know of have required to reefer to split single polyps in half and glue the desired opposite halves together. However, the fatality rate is normally very high and even if the new polyps do survive, they may lose their graft by the end of the process.
The subject of coral grafting greatly interested me for a few weeks a while back and I found a ton of interesting articles, studies, media, etc. Let me see if I can find any of those links again.