Headphone/Line out voltage for driving a LED?
Further to my comment (above) I've been thinking about how the original circuit works. The sound card outputs a 19kHz signal and we require a 38kHz signal (carrier) for the IR controller. 

In the original circuit this is achieved by connecting the LEDs in parallel so each will output on the other half wave effectively doubling the frequency and hoping the output of the soundcard was enough to drive them. 

The circuit I've come up with achieves the same (doubling frequency) effect using an NPN and PNP transistor. The AC signal is split between the two capacitors which isolate the DC input on each of the transistors. TR1 will not conduct on the positive half cycle. D1 limits the reverse voltage on the base emitter junction. On the negative half cylce it turns TR1 on and LED 1 should flash.

Similary TR2 is turned off by a negative half cycle but turned on by the positive, giving a 38 kHz flash rate between the two LEDs from a 19kHz input.

The input signal needs to exceed +/- 0.6V which should be possible from the sound card. 

If not a third transistor at the input could be used to amplify the signal level. Software stays the same. The 3V could be taken from a couple of AA cels or a 3V button cell or the 3v3 from the pi. Current taken is about 22mA when operating. With no input everything switches off so the circuit won't require an on/off switch.