Rocket launchers are very useful things to have, especially for FFYL use, but are pretty rare to find in either drops, chests, or vendors, especially in Blue or better rarity. However, there is a recipe that specifically gives you one-two weapons plus a Grenade Mod.
Coincidentially, any time after the story mission Home Sweet Home, you can open Moxxi’s Toy Box chest provided you enter Concordia via the Back Door exit (or spawn there). It contains…a Blue Weapon, a Blue Grenade Mod, and a Blue Shield (which you don’t need and can sell). Provided you have one other spare Blue weapon of any type (or save and load twice to open the chest twice), grind away for a free Blue or Purple Launcher!