Translation
I want to tell my friend that I wanna be friends with her for a long time

오랫동안 친구로 지내자
is that correct? or is there any other way to say it! formal and informally!

Question

Translation
I want to tell my friend that I wanna be friends with her for a long time

오랫동안 친구로 지내자
is that correct? or is there any other way to say it! formal and informally!

Answer

Yes, "오랫동안 친구로 지내자" is both correct and natural sounding.

You could also say:

오래도록 친구 하자.
오랫동안 변함없는 친구로 지내자. 
오래도록 우정 변하지 말자.
오랫동안 좋은 사이[관계]로 지냈으면 좋겠어요 (more formal)