OK, as promised, I'm finally here. Here are some back-of-fag-packet-calculations for you:
To calculate the resistor that each LED needs, we need to know:
Note: The "supply voltage to the LED" used in these calculations is VCC less 2 diode drops, because we're calculating the resistor required when the pin is controlling the LEDs. See Circuit Diagrams 3.2 and 3.3.
Vdrop is 0.6v
VCC is 5v
Vsup is VCC - (2 * Vdrop) = 3.8v
ILED is 20mA (most LEDs' datasheets say that this is a reasonable current).
VF is 1.9v
Vres is Vsupply - VF = 1.9v
Simple application of V=IR gives:
R = Vres/ILED = 95 ohms
"So where do I stick the resistor(s)?"
The resistor needs to sit between the centre of the two LEDs and the pin that controls them.
Normally it's not good practice to share a current limiting resistor between two LEDs, but in this case it's OK because we know that only one LED of the pair will ever be lit at one time.