This is an awkward question because an analytical reading of Section V shows that Pope only gives a reverse definition of happiness and that defining happiness is not one of his objectives. Starting at the end first, Pope declares his objective in Section V, the only Section in which he uses the word "Happiness," to be to contradict the philosophy reflected in the statement that "Better for Us, perhaps, it might appear, / Were there all harmony, all virtue here." Pope's definitive response to this idea about the order of life is to say that "But ALL subsists by elemental strife; / and Passions are the elements of Life." He further says that this order of life, such as he has associated with "elemental strife" and "Passions," is "The gen'ral ORDER, since the whole began," which "Is kept in Nature, and is kept in Man." Therefore his purpose is to dispel the idea that all is meant to be harmonious and rosy by proving that all, "in Nature" and "in Man," is strife and passion (which in Pope's era was equated with violent emotion).
Pertaining to Pope's comments in which he employs the word "Happiness," he is using reverse logic to disprove a common opinion and prove its antithesis. In the opening lines of Section V, Pope suggests a question to pose regarding the purpose and use of "heav'nly bodies," in other words, the cosmos. He puts forth a common answer to the question and labels it the response that "Pride" makes, therefore simultaneously labeling the answer a false answer, since in Pope's era, pride was a fatal sin. "Pride" says that Earth and the skies are all for "me" and "mine": "My foot-stool earth, my canopy the skies." Again, this is a false ideology that Pope intends to refute. He begins to do so by saying then in that case, if it's all for the pleasure (and happiness) of humankind, then nature has erred and is at fault: "But errs not Nature from this gracious end" (meaning: but doesn't nature therefore err). Pope claims nature has erred because there are "burning suns" and "livid deaths" and "earthquakes" and whole towns in one grave.
Then it gets a little more complicated. "Pride" answers back that nature has not erred because (1) the first "Almighty cause" acts according to general rules that are blind to individual consequences and calamities and (2), besides which, "Pride" asks the rhetorical question querying as to what in nature has been created to be perfect. Now Pope responds with a rhetorical question of his own: "Why then Man?" In other words, if nothing in nature is perfect, why suppose that humankind is created to be perfect? The answer of course is that such a supposition is impossible: humankind is not perfect.
Pope goes on to equate with "Happiness" the order that "Pride" describes and reasons forth from, and he states that just as nature errs, so does humankind err; one such error is the belief that all should be--is intended to be--"show'rs ... sunshine ... eternal spring and cloudless skies," in other words, "Happiness." He concludes his argument with the accusation that the ideological assertion that the ideological pursuit of "Happiness," equated as it is with continual natural glories and "cloudless skies," is entirely a product of pride (not surprising since the conversation has been with "Pride" all along in Section V) and charges that to "reason right is to submit" to the opposite of pride and happiness, which requires recognizing strife, passion and unhappiness as the natural order of life and humankind.