Jelly Bean and Bubblegum Parrots are a cross between a male convict and a female blood parrot. They are then usually died bright colors like, green, blue, pink, red, purple, etc.
The young fish is usually an albino variety which is chemically treated to strip the protective slime coat. They are then "painted" with dyes, and given another bath in a solution to stimulate the slime coat to grow back. Due to this torturous dying process, the fish have stunted growth, and rarely reach more than 3-4 inches. They also have a decreased life span due to the dyeing process. This also goes for other painted fish such as painted tetras.
There's been many cases of Jelly Beans and Bubblegums being able to mate and produce fry. This breeding is often mistaken for true Blood Parrot breeding, so don't be mislead by these reports.