How do I size fuses to handle sudden changes in AC line voltage into a capacitive load?
The usual solution to this is to use a slow-blow fuse. These blow only if excess current is maintained for a relatively long time. The datasheet will provide more quantitative descriptions of "excess current" and "long time".

As far as computing the peak current of the inrush current, it's probably easiest to measure. Connecting an ideal voltage source to an ideal capacitor results in an infinite current. In reality, neither the voltage source (the device's power supply) or the capacitors or the wires connecting them are ideal, so the inrush current is determined by the non-ideal inductance and resistance of all these components.

The duration of the inrush period can be calculated if you've measured the resistance, and know the capacitance. Multiply the resistance and the capacitance together, and this is the time it will take to charge the capacitor about 63% of the way to its final value. Research RC time constant for more detail.

Another option is to deliberately introduce a series component to limit inrush current. This can be a resistor at simplest, but a more sophisticated and efficient device is a NTC thermistor. By deliberately selecting your current limiting device (rather than relying on wire resistance and such), calculating the inrush current, and thus sizing the fuses, is much easier. Wikipedia has more detail under inrush current limiter.