One idea could be a story where Godzilla and Indominus Rex are forced to team up against a common, even more powerful enemy. Maybe an alien invasion that threatens to destroy their world. They start off as enemies but gradually learn to work together.
A possible plot could be that Indominus Rex somehow gets teleported into Godzilla's world. Confused and angry, it starts attacking everything in sight. Godzilla, seeing this new threat, decides to take it on. Their battle could cause massive destruction, but in the end, they might reach a truce when they both realize there are bigger threats out there.
You could also develop its character based on its experiences with the environment. If it has to struggle to find food in a certain area of Jurassic Park, it might become more resourceful and determined. It could start to explore new areas and develop a sense of curiosity about its surroundings.
The relationship can be developed through mutual need. For example, if the human is lost in the dinosaur's territory, the T - Rex could initially see the human as prey but then realize the human has some unique skills, like making fire or using tools. This could lead to a truce. Or if the T - Rex is injured, the human could use their medical knowledge (assuming some sort of knowledge transfer in the story) to help the T - Rex, and in return, the T - Rex protects the human from other threats.
Well, a funny T-Rex cartoon often has a combination of elements. Maybe it's the goofy situations the T-Rex finds itself in, or the comical way it interacts with other characters. Sometimes, it's the simple and wacky design of the T-Rex that brings the laughs.