Of currently somewhat active shops according to forum posts:
No shops currently have two-way exchanges. (IE if I have 64x I can get 1y out of the shopkeeper, where the price is 1y for 64x.)
Gold:
Haxington Oreburgh Mine: 8 ingots = 1 diamond
Andureil: ~14 ingots = 1 diamond
Ealdwine: 64 ingots = 1 diamond
Iron:
Haxington: 16 ingots = 1 diamond
Ealdwine: 64 iron = 1 diamond
Diamond:
Everyone: 1 diamond = 1 diamond
Everyone: 9 diamonds = 1 diamond block
Emeralds:
Ryebye: 1 Iron Horse Armor = 3 Emeralds
Ryebye: 1 Gold Horse Armor = 2 Emeralds
Andureil: Knockback 2 Book = 5 Emeralds
Cobblestone:
Haxington: 256 (4 stacks) = 1 diamond
Ryebye: 320 (5 stacks) = 1 diamond
Ealdwine: 384 (6 stacks) = 1 diamond
The first numbers listed are shops that have not recently been updated for a while. The last numbers are the shops that have been recently updated.