What I am about to write can be an easy OLL parity algorithm to memorize if you already have memorized the PLL parity algorithm, r2 F2 U2 r2 U2 F2 r2.
[1] Convert the middle r2 slice turn to r.
[2] Add the move F2
[3] Switch the front and top centers with either (l' U2 l)(r U2 r') or (r U2 r')(l' U2 l).
[4] F2
(For those learning K4, you're welcome, as simply converting the bold quarter turn *r** to r' achieves the mirror case.*)
Now we are going to be adding setup moves to the entire algorithm. I will show how to make a single dedge flip and also a double parity algorithm.
The Single Dedge Flip
[5] Include the setup moves r' S' and undo with S r to achieve a flip of the UB dedge.
The Double Parity Algorithm
[5] Before the entire algorithm, simply add the setup move r and undo it with r' at the end.
[6] With all of that done, it should be obvious that we need to complete half of a center with r U2 r'.
(Note: this cancels to a 16 move double parity algorithm if we convert all slice turns to wide turns.)