Hi L. Chung,
Red and green LEDs in one package have been available from LED manufacturers for many years.
Two-wire ones have the LEDs back-to-back so the two colours are determined by the polarity. If you feed it AC then both LEDs light-up producing yellow!
Three wire ones are common-cathode I think, with the two LEDs separate so they can make red, orange I think, yellow, yellowish-green I think and green.
I have an LED that alternates red and blue with a built-in oscillator.
Red, Green, Blue (RGB) LEDs are available with 3 LEDs in one package to make any colour you want.