Use the relay coil to substitute for one of the pull-up resistors in your circuit. Put a resistor, or a zener diode, or a series string of ordinary diodes, in series with the LED that turns on in the state when the relay is not energized to limit the current to 20mA for that LED. It is not an ideal solution since some current will flow through the relay coil when it is supposed to be de-energized, but probably not enough current to switch the relay (pull-in voltage for a relay is typically half the coil operating voltage). Better, since you have to add a transistor to drive the relay anyway, use the input signal source to drive the added transistor and relay seperately from the rest of the circuit.
Edit: I forgot that your LEDs are package together so you don't have access to put parts in series with only one of the LEDs. So, in addition, lower the value of the other pull-up (to be equivalent to the relay coil resistance) and put a resistor in series with the prepackaged LEDs.