I did the Pitchfork quest in San D'Oria but I'm posting what is supposed to be the way to get it in all three nations. The only one I can vouch for, though, is Sandy.
Make a party of two people. One person gets a Ghost costume (I got mine from Phamelise) and the other a Skeleton costume (my amoureux got his from Corua). Approach the huge Bomb decoration canopy-thingie near the MH in Southern Sandy and when you near it you'll both receive the Pitchfork.
In Bastok: -But I didn't do this personally- One person wears a Ghost costume and the other a Hound costume and they approach the Bomb decoration near Harmodios' Music Shop.
In Windurst -Didn't do this personally- One person wears a Skeleton costume and the other a Hound costume and they approach the Bomb decoration near the Culinary Guild.
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To get the Pitchfork +1, you go to another nation and, with the first (NQ) Pitchfork equipped, get a costume from the roaming Trick NPC who would normally turn you into your nation's enemy beastman race Orc, Quadav, or Yagudo). You will instead become a Goblin.
My two-person San D'Orian party went to Windurst and got our Goblin costumes from a Trick Specter. We then approached the Bomb decoration near the Aurastery (K-6) to each get our Pitchfork +1.
(The following is from other sources that I can't vouch for, but it's likely true. Also, there are probably other roaming Trick NPCs besides the ones posted who will give you the costumes you need.)
A San D'Orian can get a Goblin costume in Bastok from a Trick Spirit. If you're San D'Orian and got your first Pitchfork in another nation, you get a Goblin costume from a Trick Shadow in San D'Oria to get your +1 there.
If you're Bastokan and want to get the +1 in Windurst, you get a Goblin costume from a Trick Shade. In San D'Oria, a Bostokan gets their Goblin costume from a Trick Bones. A Bostokan who got the first Pitchfork in another nation and wants to get the +1 in Bastok gets a Goblin costume from a Trick Phantom.
If you're Windurstian and want to get your +1 in San D'Oria, you get a Goblin costume from a Trick Shade. In Bastok, a Windurstian gets a Goblin costume from a Trick Skeleton. A Windurstian who got the first Pitchfork in another nation and wants to get the +1 in Windurst can get a Goblin costume from a Trick Ghost.
Again, all but the way for a San D'Orian to get the NQ Pitchfork in San D'Oria and the +1 in Windurst is from other sources that I didn't verify.