Hare is echoing Kant's "*we do not make the least addition to the thing when we further declare that this thing is. Otherwise it would not be exactly the same thing that exists, but something more than we had thought in the concept*". The point of Premise 2 is that if we can conceive of God existing, but he doesn't exist, then we can conceive of a thing just like him, but EXISTING, which is then greater than him. Hare's point is that once we already conceived of God existing "we do not make the least addition to the thing" by conceiving of him EXISTING again, we have already done that. So the thing we were supposed to conceive, which was supposed to be greater than him, turns out to be the same exact thing we already conceived, not anything greater. Thus, Premise 2 is "manifestly false".

Keep in mind that in "we can conceive of or imagine God existing" Hare seems to identify "conceive" with "imagine", which is not done by everybody. Plantinga, for example, defines "conceive" as "think without contradiction", which is different from "imagine". Because we can "imagine" say time travel, even though it is contradictory. Analysis of the argument changes somewhat on this definition of "conceive", but it simply moves the error around. The [modal argument for mind-body dualism][1] is another fallacy, where the differences between "conceive" and "imagine" can get you into the weeds.  

[1]: http://plato.stanford.edu/entries/dualism/#ModArg