Curtis’ Safe Key needed to open Curtis’ Valuables Safe in Dead Island 2 can be found during/after The Final Gauntlet story quest when fast travel unlocks. To find the key, make your way over to the road near Curtis’ house as shown below.
Once there, you’ll find Crystal the Lawyer (a Screamer). Take her out then collect Curtis’ Safe Key. Head inside Curtis’ house and use the key to open Curtis’ Valuables Safe. You’ll then receive a Tactical Heavy Revolver!