There was the Blitz supercharger and Zage turbo kit for the 1NZ-FE engine in your car, both are hard to find. But for the amount of power they're going to get you, might as well drop in a Corolla engine, 2ZR-FE, it weighs the same as the engine in our car, use that as the base for your engine mod or keep it stock. The 2ZR is also the same engine in the Scion xD, except detuned by about 10HP, not sure if it's the PCM or different injectors or something, or both. It's better to look for a donor xD, as all of the parts for it are straight bolt in, with the exception of a wire for the MAF I believe, need to find a way to power it up. Check out this thread:
https://www.yarisworld.com/forums/sh...ad.php?t=56678
If you want to experiment, try the 2AR-FE from a Scion tC or RAV4. The engine I'm thinking of dropping in. This engine will be heavier though, I recommend upgrading to the 2012 SE disc rotors all around to help you stop better. And it won't be a straight bolt in, will need lots of work and experimentation if any of the OEM mount from the other vehicle would work, probably would need to fabricate them. Although the plugs to the PCM might match, it will most likely need to be rewired. The exhaust header will be up front again like in the earlier cars, and just like in the 1.0L Yaris. So don't worry the subframe already have a channel to route the exhaust.
This guy put it in an MR-S, and upped the rev limit to 8200!!! Yes, it's a 1AR-FE, but it's the same engine as the 2AR, just stroked.
And if you really want to, shoe in a 2GR-FE, then you'd have "GR" Yaris...

I've seen a picture of it in a Yaris, here you go, post #5 in this thread:
https://www.yarisworld.com/forums/sh...ad.php?t=57137
Now if you want to bite the forbidden fruit, then a KSwap...
https://www.yarisworld.com/forums/sh...ad.php?t=49933