Formal:
* Por que não? (Why not?) This is the most direct and formal translation.
* Por que não fazer isso? (Why not do that?) This is a more elaborate way to ask the question.
Informal:
* Por que não? (Why not?) This is still the most common way to say it, but can be used in less formal settings.
* E por que não? (And why not?) This adds a bit of emphasis and is more informal.
* Que tal? (How about it?) This is a more casual way to suggest something.
* Por que não tentar? (Why not try?) This is a good way to encourage someone to do something.
Other options:
* Não há razão para não. (There's no reason not to.) This is a more emphatic way to say "why not."
* Sem problemas. (No problem.) This can be used as a way to say "why not" in situations where someone is asking for permission.
The best way to say "why not" in Portuguese will depend on the specific situation and the level of formality you want to achieve.