"Happy birthday" is the standard way to say "happy birthday" in Engpsh. Some other ways you could say it include:

"Best wishes on your special day"
"Wishing you all the happiness and joy on your birthday"
"Many happy returns on your birthday"
"I hope your birthday is as wonderful as you are"

Keep in mind that the exact words and phrasing you use will depend on the context and your relationship with the person whose birthday it is.