What are the views of the five greatest theologians on the subject of happiness?

Is there some governing body that ranks theologians?

Drgb-ga,
Only Christian theologians, or also possibly Jewish, Muslim, or other ones?
Here is a short list of seven, but probably from a protestant audience:
http://www.theologicalstudies.org/greatest_theologian.html
with links to other lists. (Roman Catholics would have put Augustine
or Aquinas at the top of the list and probably not even included the
protestants.)

Jews and many of more neutral religious orientation would probably
include Moses Maimonides, and some Jews seem to consider Abraham
Joshau Heschel to be the greatest Jewish theologian of the 20th
century, others, Franz Rosenzweig.

Many sites and this quotation from a Christian one agree:
"Al-Ghazzali is said to be the greatest Muslim theologian of all time.  
He wrote the following:
'Know that the key to happiness is to follow the sunna [Mohammed?s
actions] and to imitate the Messenger of God [Mohammed] in all his
coming and going, his movement and rest, in his way of eating, his
attitude, his sleep and his talk?'"

Buddha?  Theologian or philosopher?

Im almost certain there are only 3 .....

The Good, The Bad and The Ugly.

The answer to your question may only be found once you have decided
who YOUR 5 greatest theologians are. And the basis upon which you
choose your 5 greatest thelogians will influence the outcome of the
question, so why not ask yourself the question and draw your own
conclusions? Then you can take the credit for a job well done :o)