I have lots of two-pin bi-color LEDs around here... These two-pin red-green LEDs are available from DigiKey. They should be readily available from Bangood or EBay.
If you must use a three-pin LED, it would be easier to redesign the circuit to use a common-anode, rather than a common-cathode one like you show.
If you must use a three-pin LED, it would be easier to redesign the circuit to use a common-anode, rather than a common-cathode one like you show.