Modem
The max current for the IR LEDs requires the datasheet for that part. Usually, the pulse current on an LED is quite high. The only way to kill an LED is to drive the current really high constantly.
If you continue to run from the serial port's power, I think this power source will limit you long before the LED's spec becomes an issue.
From the 2N4401 datasheet, you can use either the Beta min of 40 or look at the curves for a typical collector current and choose beta from there. From the Fairchild datasheet, 150 is a typical value. I realize that these two numbers differ by almost 4X. The reason is that in switching circuits, you drive the transistor into saturation and allow the collector load to determine the current rather than the base drive. With the circuit as it is, beta = 150 means the transistor will attempt to sink up to 64.5mA. With the minimum beta of 40, 17.2mA of collector current.
Use an oscilliscope and look at the waveform at the collector of Q2. If the collector drops within a few hundred milli-volts of gnd, then the collector drive is fine and increasing the base current will not get you any additional range.
Overdriving the transistor has its own problems. First, you waste more power in the base junction and you do not have power to spare. Secondly, the deeper into saturation you drive the transistor, the longer and slower it is turning back off.
If I was trying to tweak this circuit, I would look at eliminating the MAX232. On the transmit side, this part inverts the signal and limits it to 0 to 5V. However, you have spare gates in the 4001 to do the inversion and the limits can be done with two diodes and a resistor. On the receive side, the MAX232 again inverts the signal and then shifts it to about +-10V per the RS232 spec. However, it is widely known that on cables under six feet, RS232 works fine at 0 to 5V. Therefore, you can either use a BJT to perform the inversion, or incorporate the inversion back in the PIC. (The MAX232 consumes power running a charge pump and its internal circuitry that you could be using for the IR LEDS.)