If you know of a site where this is written up nicely, please let us know. Otherwise I will try to write it up as much as I can and then somehow discuss it with you. This topic of algum / cada|todo / nenhum / qualquer and their negations and synonyms (with the more or less matching english expressions and the peculiarities of both) deserves at least a nice table with annotations.
If you mean "not any car (at all)", it's certainly "nenhum carro".
- Não pode ser nenhum carro/carro nenhum (yes, with double negation) = It can't be any car (at all)
- Não pode ser qualquer carro/um carro qualquer = It can't be just any car (, it must be a special car).