Does it need to be one word? 'shit' here wouldn't fit in any case. What about 'care at all'?

There are lots of options. Go to books.google.com/ngrams and search for "don't care a ": *fig, bit, pin

If you just want a loophole around vulgar language, try "don't shive a git". If you want something more esoteric, consider "don't care a rad". Rad being one of the units used to measure radiation.

"damn", "dang", "darn" still too offensive? What about "fuck" alternatives (fork, funk, fudge)?

Line 2 should be In much too short a day, no?

If that's supposed to be a limerick, then there is no alternative. A true limerick has to contain offensive words, preferably in the last line.

It is not a limerick, it is a ballad. The rhyming sequence goes ABAB. Plus, since it is for school, a cleaner alternative is always a better alternative. There are a few more verses, but I felt no need to include them all.

@T.E.D. - "A limerick packs laughs anatomical/into space that is quite economical/but the good ones I've seen/so seldom are clean/and the clean ones so seldom are comical" -- Isaac Asimov.

@JeffZeitlin - My personal favorite example is the one that turns a haiku (talking about nature, as is required) into a limerick by adding a final line of "poopity poopity poop."

@T.E.D. You can't turn a haiku into a limerick by just adding a line. Haiku is 5-7-5 syllables, limerick is 9-9-6-6-9.

@rackandboneman All of those are completions for "don't give a _____"; "don't care a _____" doesn't make much sense with any of them.

There's more to writing a poem than rhyming. The last two lines are far too long (or the first two lines are far too short), so your poem doesn't scan well at all.

@chepner - While I appreciate your help, in my question I was only asking for alternative words, and not a review of my poem. Thanks anyway!

It's astounding that not one person here gave the obvious, ubiquitous answer in US English, "toss". Don't give a toss. The fact that "whit" got votes suggests every single user of this site is, what, 90? 110? years old. Wild stuff!

Just BTW @TarynLambert, I really like your poem. Fantastic. Do you have any musical friends with a band, ideally a badass band, have them put it in a song dude. It reminds me of Surrender by Cheap Trick.

@Fattie Lived in America all my life, and “give a toss” sounds vaguely British to me. “Ubiquitous” it is not, at least in my experience (I’ve lived in NYC, LA, DC). And while “whit” certainly isn’t either, I have seen it used as a stand-in for “shit” that’s easily understood as being just that—where “toss” just sounds foreign to me and I wouldn’t be sure if it was vulgar itself, bowdlerization, just not vulgar; I just wouldn’t know. And for the record, I’m substantially younger than, say, Cheap Trick.

@Fattie - While I have never heard of "don't care a whit" before, I liked how it goes in my poem. While it is relatively old, it is easy to understand in my context. And I am most definitely not a 90 year old., if you could not tell from the content of my poem. And thank you for liking my poem.

@KRyan - you know, you're right that ".. give a toss" is a bit British. But (just one man's opinion - maybe I'm old) all Americans know it. However I'm afraid I feel that "whit" sounds totally (if anything) British - it sounds like you're trying to talk like Churchill or something. It's like saying "old chap". It's a "ye olde..." word. Anyway, good point.

Actually there's probably a real estate development near here called "Whit Pointe...."

Or "Old Whit Town." Or "Whit Meadows." :)

@Fattie I'm an American, and I didn't know it until I read your comment. I'm better there's more out there. Also, why are you answering in comments? I mean, seriously. If it's a common British phrase, you could be earning some reputation points on a HNQ.

maybe a bit? or a brit? or a (Geiger-Mueller) kit?

@Fattie It's astounding that not one person here gave the **obvious, ubiquitous** answer in US English, Well, we were obviously waiting for you to write it. You seem to have a lot of input to offer, why don't you write an answer?

Please include the research you’ve done. Questions that can be answered using commonly-available references are off-topic. A Google search for "don't care a" throws up several of the LMGTFY answers given below, including entries in dictionaries.

IIRC in British, "toss" is slang for sex. (Hence the word "tosser".) Still at least as vulgar as "give a damn".