Period 2 Reversed Quine
RProgN, 3 bytes
1
2

Thanks to @MartinEnder for reminding me about this answer.
Try it online!
How it works
This exploits a potential flaw in our definition of proper quine:

It must be possible to identify a section of the program which encodes a different part of the program. (&quot;Different&quot; meaning that the two parts appear in different positions.)
Furthermore, a quine must not access its own source, directly or indirectly.

That's obviously the case here, as the output is the reverse of the code and the code is not a palindrome.
RProgN – reverse programmer notation – uses a LIFO stack and prints the items on it in the order they are popped. The two tokens 1 and 2, separated by spaces and/or newlines, get popped in reverse order and are printed separated by a newline.
This prints the reversed program
2
1

which, in turn, prints the original one.
!enilno ti yrT