How to use 2 TSOP1738 (infrared sensor) in one circuit?
Yes, both are common emitter output and can share 1 pullup R.

But your supply voltage AC noise ought be &lt; 1mV  for best range. ok?

That means the LED may need a separate V+   path to source and ground path must not drop mV to avoid long range Rx noise during detection.

Add a low ESR bulk e-cap to Vcc,Gnd,  100uF?

But 100uF load wont work well on output as the cap will draw large currents.
Ic=CdV/dt
 You need a transistor on outputs to boost current or better CMOS 1 shot to buffer IR Rx then stretch pulse with diode, 1uF, 1Meg decay  then output 330 to 1K from CMOS Inverter to LED.