I don't know of any in that price point that I would reccomend. That said, the Leupold Yosemite binoculars can be found for $80 a few times a year. The 6x30 and 8x30 ones are actually quite nice optically, have a wide interpupillary range (can fit adults and kids alike), I think I've even seen some in pink before if that matters to her, and have a lifetime warranty. I've never used their 10x variety. I used them for a long time and have actually worn out the focus knob on three pairs only to call Leupold and have them send me a free of charge replacement and told me to keep the old pair too (which I gave to local kids).
I no use a pair of 8x30 Swarovski binoculars but still keep some Leupold Yosemite's around for loaners and to be honest even after getting used to Swarovski's I wouldn't be upset to take the Yosemite's into the woods again. For a kid, I would recommend the 6x as it will appear more steady in the hand at a lower magnification and they won't miss the power of the 8x or 10x. While I haven't looked through their 10x variety, I would imagine those get dark pretty quickly in fading light compared to the others due to exit pupil.