Sorry, my replies are not always quick. I have some administrative work to get done.
Correct, a PC PSU is of little use. Rebuilding it is far too much work.
In theory, you can add a dual voltage boost converter but it is more expensive than constructing a real dual voltage power supply the way we know will work.
In principle eight 18650 Li-Ion batteries (4 for each rail) can be used at least for test if the amplifier works. You should put good buffer capacitors on each rail as experience is that such batteries are slow in reacting to the dynamic current demands of an amplifier.
LM7818 and LM7918 have a max. current of 1.5A which is clearly insufficient for a 2x50W amplifier.
I guess you would like a cheap power supply solution that almost guaranteed works with the amplifier. My way of solving such a need: Buy (or get for free from an electronic recycling station / dump yard) an old (20-30 years) second hand "midi-stereo-set" with an output power of some 30W in 6 Ohm. I typically pay some 7 EUR including speakers. Remove the power supply and re-use it for the TDA8922 amplifier. The best (and cheapest) are the 20-30 year old sets using a real net-transformer because they are very simple in design and easy to identify the useful components in.