Most slowdown stuff when you see it for trainers is either rapid fire press start like a slowdown mode on controllers give you, or they flood the CPU with instructions such that it has to slow down to process those. For some newer stuff I imagine you could also underclock it.
I don't think there is anything for the PS3 here, and likely any underclocks available are not going to be enough to do something useful in this. Not sure how easy it would be to slam the CPU with do nothing instructions to cause slowdown but that would not be the worst, though given how heat prone a lot of PS3s are I would be sparing in this.
This then means you get to hack a game properly if you want this sort of thing. Much the same idea as speed up, though in this case you will not be disabling vblanks but maybe only getting it to render every other one (simple enough add some code that checks a given area, skip if 1 and reset that to 0 after that, if 0 then at end of vblank (or at least after the check) then set it to 1).
After that any slowdown/speed options within the game itself; text speed might be a variable rather than a setting. Then any animation aspects where you move half the speed for everything and possibly adjust timers, and probably want a similar IF 1 then ELSE do this thing like above. This sort of thing will be a more involved hack.