Romans 12:10 Be kindly affectioned one to another with brotherly love; in honour preferring one another
Seems to me that is what saying happy birthday is - recognizing and honoring another.
another thought:
Romans 14:5-8 One man considers one day more sacred than another; another man considers every day alike. Each one should be fully convinced in his own mind. He who regards one day as special, does so to the Lord. He who eats meat, eats to the Lord, for he gives thanks to God; and he who abstains, does so to the Lord and gives thanks to God. For none of us lives to himself alone and none of us dies to himself alone. If we live, we live to the Lord; and if we die, we die to the Lord. So, whether we live or die, we belong to the Lord”