Since you refer to "Diodes" then I then you would be referring to Infra-red emitting LEDs -- short lead is anode, long lead is cathode.
** Flat side of plastic base is oriented towards the cathode. **
See page 3-16 of the Junk Yard manual for orientation of the LEDs.
This manual can be found on ipdb.org

But if you are referring to the receiver board then those are phototransistors (not diodes).
For the receiver board's phototransistors -- short lead is the emitter, long lead is the collector.
** Flat side of plastic base is oriented towards the emitter. **
See page 3-17 of the manual for orientation of the phototransistors.

This assumes you are using QED123 (IR emitter LEDs) or equivalent and QSD124 (IR phototransistors) or equivalent.
Since you don't mention the part number of your new replacements, this is as close I can get.