If I spell doing as doin' then how should I spell doings?
Would it simply be doin's?
How you doin'? [Friends] Ha!
I would distinguish the usage of "doin" from "doin's". The context in which "doin's" is the word to use is likely to be much different, and much less frequent, than "doin'", which will come up in casual conversation with some frequency, as with - "Watcha doin'?" The usage of "doin's" is likely to be entirely unrelated.
'Doin's would often be dialect, as with literature. The best known example is possibly from "The Turmoil" (1915), by Booth Tarkington.
"Ev'ything got look spick an' span fo' the big doin's to-night," Bibbs's guide explained, chuckling. "Yessuh, we got big doin's to-night! Big doin's!"
Certainly, it shouldn't be difficult to find numerous examples from works in the pickaninny dialect.
"Like her pap, all big noise and no big doin's."
"Imitation of Life", Fannie Hurst
However, I surely do not think usage need be racial caricature. One ought be careful, though, to ensure that usage captures a character's voice, avoiding the perception that it is contrived, or otherwise forced.
"Big doin's" is in the language as a rural, country expression.
"Ham Nation", "Big Doin's in Starkville"
[Oops. I don't have the reputation to use this third link:]
I reckon those examples ought help. I'm fixin' to chow down the wife's fine cookin' here in a bit, so got to go. Catch y'all later.