How to make stronger colors in three part pannacotta?
All of these are natural colorants but also impart a bit of flavor with them.

For the raspberry layer you could use a tiny amount of beet juice to really kick the red.

For yellow colors you have a few options. Saffron can work really well though I'm not sure what mango/lime/saffron tastes like.  Another organic single ingredient is Achiote, which has an extremely mild sweet flavor. It's used for coloring mac and cheese and most processed cheese.

Hope these ideas help.