Place the chicken breasts in the bottom of a 5 quart or larger slow cooker. Drain the black beans and add them to the slow cooker along with the salsa and corn. Add 1/4 cup water, plus the minced garlic, chili powder, cumin, oregano, cayenne, some freshly cracked pepper (about 10-15 cranks of a pepper mill).
Give the ingredients a brief stir to distribute the spices. Secure the lid on your slow cooker and cook on low for 8 hours or high for 4 hours.
After 8 hours on low or 4 hours on high, carefully remove the lid of the slow cooker. Stir with a fork to shred the chicken (it should be very tender and will shred easily). Taste the chicken mixture and add salt if needed.
To build the bowls, place one cup of rice in the bottom of a bowl and top with 1 cup of the shredded chicken mixture. Top with a little cheddar cheese and a sprinkle of sliced green onions.