Here’s a vibrant color gradient palette suitable for a cartoony UI, incorporating dark gray/black, orange, off-white, and red.

 <Cartoon Vibes>
1. Dark Charcoal - 
                            
                            #2C2C2C
                         - A rich dark gray that sets a solid foundation for the gradient.
2. Bright Orange - 
                            
                            #FFA500
                         - A lively and energetic orange that adds a playful touch.
3. Soft Off-White - 
                            
                            #F5F5F5
                         - A warm off-white that lightens the palette and provides balance.
4. Vivid Red - 
                            
                            #FF4500
                         - A striking red that brings a sense of excitement and attention.

This palette is designed to create a cheerful and engaging atmosphere, perfect for a cartoony UI. The combination of bright colors against dark tones helps elements stand out, ensuring a fun and inviting user experience.

Would you like further customization or additional shades? Or do you need guidance on how to implement this gradient in your design?