Do these two sentences have the same meaning?
Happliness is having you to believe in me. -- This means that I needed someone to believe in me, and you do that, so that makes me happy.
Happliness is having you who believes in me. -- Not grammatical.
Happliness is having you, who believes in me, in my life. -- Not very natural, but you are happy this person is in your life, and that this person believes in you.
Happliness is having you believe in me. -- This is different from the first. It implies this person is very important to you, and the fact that he or she believes in you makes you very happy. This may be what you meant all along.
Please note that English sentenes between with capital letters and end with punctuation marks.
Student or Learner