Allspice is propagated by grafting. Plants are dioecious (some trees are male and some are female) so you plant the seed and graft budwood from a female tree onto the rootstock. (Otherwise half of the trees would not bear fruit.). ECHO has tried to propagate allspice by cuttings but even when done under mist we did not succeed.
Nutmeg is also dioescious. It can be propagated either by grafting or air layering.
Cinnamon and cloves are both propagated by seed. I’ve also seen cinnamon propagated by air-layering (also know as marcottage).