Unfortunately, I can't really choose neither the protocol, nor the LED. But the question is, on which time can I average this? Over the message? Over the time from the start of a message to the start of the next message?
This can be averaged any time as long as the max. pulse width limitation isn't exceeded. Its normally done for each and every pulse. You can get the max current ratings and max pulse duration at peak current hopefully from the datasheet.
See page 3 here for absolute maximum ratings on some typical IR LEDs. I'm familiar with the OP293, which has a free air continuous forward current of 100 mA and peak forward current (25µs pulse width) of 2.0 A.
If being pulsed at 2.0A, 56KHz, 50% duty cycle, it would be on 9µs and off 9µs. Although below the 25µs max pulse width, it averages to 1.0A continuous - this exceeds the 100mA continuous limitation.
Therefore, Max duty cycle % = (Continuous Current/Required Pulse Current) x 100
So for the OP293 with 2A impulse, it would be 5% duty cycle or 0.9µs maximum on time with 17.1µs off time.
Hope this helps.