Use a single gate Schmitt Trigger relaxation oscillator. I don't know if it will be suitable for that application or have desirable properties like stability, but it is simple and it is cheap.
Close to 40khz is usually good enough though a trimmer would be a good idea.
The simplest one I know of is a Schmitt triggered inverter with a capacitor to ground on the input and the output fed into the input via a resistor.
The bellow link contains a lot of basic logic functions and several useful pulse generators/stretchers using only basic passive components and Schmitt inverters.
For IR it's not at all critical, but for ultrasonic it needs to be accurately set to the frequency of the transducer - you MUST have an adjustment to do this.
Three suggestions:
1) Check out the Fairchild app note AN-118 on CMOS oscillators;
2) Consider using a single PIC chip -- I used a 12F509 for oscillator, modulator, and receiver; parts count was very low compared to making something from the 555 or 556 chips; and
3) See attached schematic for a 38KHz IR oscillator and modulator based on the 556 chip.
In the 556 design, R1/C3 gives approximately 38KHz.
Just my $0.02 but a relaxation oscillator with an adjustment seems way simpler then any of the alternatives. Any two chip solution obviously fails the simple test. The requirement was not that the solution work well or even work at all. The absence of the last requirement makes this whole exercise a bit artificial.
Referencing back the the original queston, I assumed the OP would also need modulation of the carrier for any practical purpose using one of the current, receiver-demodulation devices like the Vishay series devices. The 556 is "one-chip" ; although, I wouldn't argue that point very far. There are so many problems with simple on-off IR that I thought it better to steer the OP in the direction of modulationg the carrier.
Here's the one-chip solution for carrier and modulation, as well as receiver, that I mentioned earlier. I believe it meets the definition of simple, but unfortunately, it uses a PIC. The code is not secret, and I will happily provide it to anyone with a small warning. It was my second attempt post-blinking LED. Therefore, it works, but is not pretty.
John
After wondering for a bit, i thought this might be a violin string.
Then i thought maybe a small whistle,
this would have no moving parts.
Except the air i suppose, but thats not part of the whistle.
If there is a simpler oscillator,
then i haven't thought of it.
well, you could keep dialing it until you found the 40k frequency. then you would measure the resistance and you could use resistors with that value in place of it.
The datasheet for a 555 has a formula to determine the capacitor and resistor values. These parts might have a 5% tolerance so the 40kHz might be anywhere from 36kHz to 44kHz.