Heat sauté pan over medium heat. Add enough oil to lightly cover bottom of pan, about 1 tablespoon. Add onions, peppers and garlic and sauté over medium heat until onions begin to brown, about 5 to 8 minutes.
Add lime juice, lemon juice and vinegar. Bring to a boil, add cherries and mangos. Simmer for 8 to 10 minutes, stirring occasionally. Remove from heat. Place in a serving bowl and chill.