36 cards where it’s legal in Legacy and the card types include “goblin” and the mana value = 2 and the rarity is equal to uncommon

Akki Raider (Betrayers of Kamigawa #92)
Battle Cry Goblin (Adventures in the Forgotten Realms #132)
Bloodmark Mentor (Duel Decks: Knights vs. Dragons #50)
Cheering Fanatic (Battlebond #58)
Dragonlord's Servant (Forgotten Realms Commander #123)
Ember Hauler (Core Set 2020 #137)
Enterprising Scallywag (The Lost Caverns of Ixalan #148)
Enthusiastic Mechanaut (Kamigawa: Neon Dynasty #218)
Goblin Airbrusher (Unfinity #108)
Goblin Archaeologist (Darksteel #63)
Goblin Cratermaker (Guilds of Ravnica #103)
Goblin Fireleaper (The Lord of the Rings: Tales of Middle-earth #133)
Goblin Glider (Eighth Edition #189)
Goblin Wardriver (Duel Decks: Merfolk vs. Goblins #50)
Grim Wanderer (Adventures in the Forgotten Realms #107)
Invasion of Mercadia // Kyren Flamewright (March of the Machine #147)
Invasion of Mercadia // Kyren Flamewright (March of the Machine #147)
Kyren Legate (Mercadian Masques #197)
Mogg Jailer (Planeshift #68)
Mogg Maniac (Tempest Remastered #147)
Mogg Squad (Tempest #192)
Munitions Expert (Modern Horizons #209)
Picnic Ruiner // Stolen Goodies (Wilds of Eldraine #232)
Skirk Drill Sergeant (Duel Decks Anthology: Elves vs. Goblins #49)
Slavering Nulls (Duel Decks: Ajani vs. Nicol Bolas #45)
Sokenzan Smelter (Kamigawa: Neon Dynasty #164)
Spike Jester (Dragon's Maze #106)
Spitfire Handler (Onslaught #236)
Sprouting Goblin (Dominaria United #145)
Squeaking Pie Sneak (Lorwyn #142)
Tattermunge Witch (Modern Masters 2017 #212)
Thick-Skinned Goblin (Time Spiral Remastered #196)
Vial Smasher, Gleeful Grenadier (Outlaws of Thunder Junction #235)
Warren Weirding (Morningtide #82)
Wily Goblin (Ixalan #174)
Zhur-Taa Goblin (Ravnica Allegiance #215)
Zoyowa Lava-Tongue (The Lost Caverns of Ixalan #245)

This search is finished. Now the real work can begin.