Melt coconut oil over medium-high heat in a large frying pan. Add onion, carrot, and garlic; stir-fry until tender, about 3 minutes. Add shrimp and ham; stir-fry until shrimp are almost cooked through, about 2 minutes. Add rice and soy sauce and continue to cook and stir for 1 minute. Season with salt and pepper and remove from heat.

Stir pineapple, tomato, and green onions into fried rice mixture until thoroughly combined.