Me, too. "Congratulations on your birthday" is rather stiff, but an acceptable birthday greeting--and a literal translation. I reported this.
But it gets me to wonder: is おたんじょう日おめでとう also a friendly, casual/familiar birthday wish? Is there something more formal that we should know about?
Well, okay. This sentence is dumb! Its face looks like a smelly butt! It cuts its own hair and wears whatever the thrift store couldn't sell! It's on the wrong side of 40 and it will never find true love!
（お）たんじょうび = birthday
おめでとう = congratulations
...or literally "birthday congratulations," which is better understood as "happy birthday" in English.