Made a tasty sauce with some fresh leftover pineapple a few weeks ago. The acid here will help it keep well, like a ketchup.
2 cups fresh pineapple, cubed
1/2 cup sugar
1/4 cup water
1 tbsp. minced ginger, or 1 tbsp ginger juice.
1/2 cup fresh orange juice
1/4 cup ketchup
1 tbsp. white wine or cider vinegar (unseasoned rice vinegar is optional)
1 tbsp lemon juice
Pinch red pepper flakes (optional)
Salt to taste
In small saucepot, heat pineapple, sugar and water, and ginger juice. Cook for 15-20 minutes until pineapple is soft. Remove from heat, add pineapple to blender and blend until smooth. Add back to saucepot, and whisk in, ketchup, vinegar, lemon juice, and optional chili flakes. Heat for 5 minutes. Adjust seasonings to taste. Strain and serve.
Customize it: consider adding some lime juice, or some fruit zest.