For the pomegranate seeds, I would definetely recommend the national Mexican Independence Day dish: Chiles en Nogada. They are truly delicious. They can also be added to bulgur pilafs and salads, as suggested before.
Papaya is yummy just with a bit of lime juice, Greek yogurt and honey on top for breakfast or dessert. Enjoy!
One of my favorite dishes combine the two but seperate in a way. I make a papaya salsa or salad. Mango, cucumber, red pepper, onions, jicama and pears tossed with a sweet pomegranate vinaigrette. This was served with grilled chicken and a mashed pomegranates. I basically found a recipe to mash them add some garlic and a little fruit juice to thin it out. I also added some pear and a bit of honey. It was almost like a cranberry like sauce. Just a little on the side was a nice tart accompany to the sweet and cool salsa of the mango Very tasty. The chicken was just grilled with salt, pepper and a dash of cumin I believe.
A bit late, apparently, but for next time: A Thai restaurant I ate at in Seattle served my meal with a small salad on the side that was thinly julienned papaya, carrot, and red onion, with very thin rings of thai chili pepper (serrano or jalapeno would work, and either would be less spicy) and some cilantro leaves. It was all raw, crunchy, spicy, sweet, and delicious. :D
Papaya and onion grilled with some olive oil s/p and then diced up. Mix with some of the pomegranate seeds, a light citrus vinaigrette as use as a wonderful salsa served over baked chicken I would use some ground walnuts or pecans, some bread crumbs and some fresh cilantro, lightly breaded and baked or you can pan saute if you want. Add the wonderul roasted fruit salsa over the chicken. Healthy and quick and easy
Grilled mango just with s/p is wonderful over chicken and fish
Pomegranates great in salad dressings on on salads with goat cheese apples, pears, walnuts a savory blue cheese dressing. Lots of possibilities.
A fresh pomegranate seeds sauted with apple juice and port wine is amazing over a grilled pork tenderloin stuffed with crimini mushrooms and goat cheese. Stuff the pork, grill and then top with the reduction of a pomegranate wine and fruit glaze.
Mash up a couple of seeds, add to vodka, some oj and a great cocktail
For the papaya, I vote to let is stand on its own. A wonderfully ripened papaya is truly hard to beat. Is it ripe yet, what does it look like?
As for the pomegranate, they, too, can be fun to eat. The seeds are great additions to salads. And I am sure a quick search will lead you to some jam or syrup recipes. Homemade pom syrup over a crisp waffle...mmmmmmm.