I think the most common way to say ‘I want to be happy’ is “shiawase ni naritai”. The expression “ureshiku naritai” is grammatically correct but I don’t think this is something that most Japanese people would use. (source)
I got a friend who speaks Japanese and lives in Japan, but is not a native speaker, to confirm the translation for me; but even if I had known this I probably would have gone with “Ureshiku Naritai”, since it’s an allusion to “Tsuyoku Naritai”.
For those wondering about the article’s title:
I got a friend who speaks Japanese and lives in Japan, but is not a native speaker, to confirm the translation for me; but even if I had known this I probably would have gone with “Ureshiku Naritai”, since it’s an allusion to “Tsuyoku Naritai”.
Ah, thanks. I missed the allusion.