You can probably power the IR emitters at 200mA but only for short periods.
Use a 555 timer with the LEDs connedted from the positive rail to pin three and set the current at 200mA for a duty cycle of 90% high at 30kHz. As the timer is acting as a current sink then the actual duty cycle for the LEDs will be 10%. Also and don't to allow for the saturation voltage on the 555's output when calculating the current.
Connect the detector to a missing pulse detector (use another 555, the circuit is on the datasheet).
You could use a 556 dual timer if you want to save space time and money.