What would be the onomatopoeia for "spit"?

Solution 1:

ptui! - expresses disgust; usually accompanied by spitting

For example...

...she coughed and corralled the rattle in her chest into her mouth then ptui! - spat on the ground

There aren't many examples of the verb form (as with the cat meowed, the dog woofed), but I did manage to find this one...

Spit should be blown, not ptuied weakly with the lips, which often results in dribble.

OED (subscription-only) don't list the spelling ptooey , but they do have this in their entry for...

ptui
Chiefly N. Amer.
Etymology: Imitative. Compare pfui int., phooey int., and also ptish int., pshaw int., etc.

Solution 2:

The most common word is probably

ptooey: an imitation of the sound of spitting [Collins]

It is also spelled ptui. In fact, this spelling is more common in both the British and American English Google Books corpora according to the NGram, but for whatever reason I'm finding the ptooey spelling easier to find in published media, from CSM to The New Yorker. Both spellings are playable in Scrabble.