The Cherokee syllabary [0] and the Canadian Aboriginal Syllabics [1] are both scripts designed for use with North American indigenous languages, and both are still widely used (relative to the usage of indigenous languages in general).
> the one given to them by their English-speaking colonizers with had they been given any in the first place
Well, history is complicated: it's certainly true that the vast majority of the colonizers were trying to ban the indigenous languages, but there have always been a few people working with the local groups to understand and develop their languages, even hundreds of years ago. And over the last 50 years or so, there's been lots of support for language preservation and education.
> and not been all but exterminated instead
I'm not sure if you're talking about the languages or the people here, but there are some 6 million Indigenous people [2] and 700k speakers of indigenous languages [3] [4] [5] in North America today, so I wouldn't quite call either "all but exterminated".
[0]: https://en.wikipedia.org/wiki/Cherokee_syllabary
[1]: https://en.wikipedia.org/wiki/Canadian_Aboriginal_syllabics
[2]: https://en.wikipedia.org/wiki/Indigenous_peoples_of_the_Amer...
[3]: https://en.wikipedia.org/wiki/Indigenous_languages_of_the_Am...
[4]: https://en.wikipedia.org/wiki/Languages_of_Canada#/media/Fil...
[5]: https://en.wikipedia.org/wiki/Languages_of_the_United_States...