No Earth has been assigned to the Super Friends in Morrison’s Multiverse.
(I will comment at the end)
But back in the day the Super Friends had an Earth. This is from Super Friends Wiki:
One of the most striking elements of this reality was that its heroes were absolute paragons of virtue, with no fault or flaws to speak of. They were incorruptible and wholly committed to helping others while preserving the doctrines of “truth, justice and peace for all mankind.”
The naming of the universe of the Super Friends franchise is a bit complicated. When the Super Friends comic first came out, E. Nelson Bridwell wanted the setting to be Earth-One. There were multiple references to other comics that were clearly set on that Earth, and there were even stories that firmly named it Earth-One. However later episodes of Super Friends and also DC books made it impossible for the Super Friends to exist in that Earth, which at the time was the mainstream world of the DC Multiverse. One thing is for sure though, that the Super Friends consider their Earth Earth-One, no matter what otherworlders call it.
Because of the obvious fact that the two Earths were in different universes, fans used the name Earth-1A while Bob Rozakis suggested the name Earth-B for the universe that the Super Friends franchise took place in.
Some people included DC’s humor comics (like the the Inferior Five) as part of Earth-B while others listed it as a separate reality called Earth-Twelve. In any case E. Nelson Bridwell was the writer of the Super Friends comic series which clearly put it on “Earth-B” and since it tied into the Super Friends television show, that also took place on “Earth-B”. More recently, Super Powers comics volumes 1-3 were formally assigned to Earth-Thirty-Two . It stands to reason because of this, the universe that the Super Friends were part of was indeed Earth-Thirty-Two .
Since stories that happened after Crisis were assigned to Earth-Thirty-Two (including DC Challenge #5–12 and Batman: The Last Angel, 1994) it’s clear Earth-Thirty-Two was not part of “another corner” of the multiverse seen in DC Comics. This is also clear, in that the Crisis on Infinite Earths also happened in the Superfriends reality, and not only that, it happened from the same perspective as it did for Earth-One in the comics.
In other words, Earth-One had a similar Crisis in another corner of the multiverse, with this version of Earth-Two. That was shown in DC Comics. However, on another corner of the multiverse, another Earth, also called Earth-One by the local Super Friends, or Earth-1A or Earth-Thirty-Two ; also had a completely identical Crisis, but it instead involved this version of Earth-Two, or Earth-2A.
What this tells us is quite a bit, and that’s that the DC Comics Earth-One and the Superfriends Earth-1A, or Earth-Thirty-Two or whatever we’re calling it, are very much distinct realities, but they share a common history. This has been demonstrated again and again. And yes, the Superfriends comics have referenced other DC Comics that were also set on Earth-One as well. This also doesn’t mean that they are one in the same, just very similar. Even the Super Amigos Comic Books and the Super Powers comics have complete reprints of DC stories; but that doesn’t make them part of that continuity. They just have a similar history.
Another way to illustrate this is this way: In the Super Friends coninuity, many events happened that also happened in the comics; such as the Crisis on Infinite Earths, Destruction of Krypton, the Park Row tragedy and the origin of Superman. Are we to assume that since those events happened in both continuities that they are one and the same universe? Of course not. If we did, we might as well say that the Nolanverse is also part of the Super Friends continuity, since it had the Park Row tragedy as well, and can anybody actually name a continuity in which Krypton didn’t blow up? It would be silly to say such a thing, because these wouldn’t be compatible.