How do you say "we only have one carrot left"?

TL;DR Attempt 4 should be what you are going for.

---

I'll attempt to analyze it linguistically:

First, we need to confirm the sentence follows the SVO structure, which is used in Standard Chinese.

In English, the past participle "left" is used as an adjective, thus we have the following:

• S: We
• V: have
• O: one carrot

However, in Chinese, 剩下 and 只有 are both verbs. Thus, using both at once would logically require multiple clauses. Now, we can eliminate sentences that does not obey the SVO pattern. Be careful of invisible part-of-speech conversions (轉類) in Chinese.

• Attempt 1: 我们S 只有V 一个红萝卜O 剩下V。 Incorrect. It is fine using this informally, but this should be grammatically incorrect.
• Attempt 2: 我们S 只有V 一个(剩下的 adj)红萝卜O。Correct
• Attempt 3: 我们S 只有V 一个(剩下着 adv)红萝卜O。Incorrect. Only adjectives qualify nouns. Adverbs qualify verb. Also, I haven't even heard of "剩下着" as an adverbial phrase.
• Attempt 4: 我们S 只剩下V 一个红萝卜O。 Correct
• Attempt 5: 我们剩下的S 只有V 一个红萝卜O。 Correct

---

So preliminarily, Attempt 2, 4, 5 are grammatically correct.

Let us analyze the grammatical sentence structures:

Attempt 2

          我们   只  有   一个  剩下的   红萝卜。
Level 1:  -S/  --------Predicate--------/      A: Adverbial
Level 2:        A/H/  -----Object------/      P: Predicator
Level 3:           P/  -M-/---Head-----/      M: Modifier
Level 4:                     -M/的 -Head/      H: Head

*A-H structure is formed with an adverbial (adv.) and a predicator. M-H structure is formed with a modifier (adj.) and a noun/complement. A numeral-classifier (一个) is analyzed as an adjective.

From this analysis, we can see we can approach this context from the most general to the most specific meaning:

1. We have a carrot.
2. We only have a carrot.
3. We only have a carrot that is remaining.

Attempt 4

          我们    只    剩下     一个     红萝卜。
Level 1:  -S/   --------Predicate---------/
Level 2:         A/-Head/    ---Object---/
Level 3:               P/     -M-/--Head-/

The context:

1. We have remaining a carrot.
2. We only have remaining a carrot.

Attempt 5

          我们剩下的    只  有     一个     红萝卜。
Level 1:  Subject/   ------Predicate-------/
Level 2:              A/H/    ---Object---/
Level 3:                        -M/--Head--/

*This subject uses "Normalization", a technique in grammar to transform a verb into a noun. Here, "我们剩下的" means "What we have remaining". Otherwise, you may treat this as missing the Head in an M-H construct: "我们剩下的(材料)" The ingredient we have left.

Context:

1. What we have remaining is a carrot.
2. What we have remaining is only a carrot.

---

Now, with the context already laid out in English, it is not hard to understand the different nuance of the several grammatically correct attempts.

• Attempt 2: We only have (a carrot that is remaining).
• Attempt 4: We (only have remaining) a carrot.
• Attempt 5: (What we have remaining) is only a carrot.

As you can see, each of these sentences have the idea "remain" in different sections of the sentence.

• Attempt 2 focuses the carrot. How is the carrot? What is the state of the carrot?
• Attempt 4 focuses the action.
• Attempt 5 focuses the subject.

Attempt 4 should be what you are going for.

---

Conclusion

In general, sentence structure analysis is really useful in discovering the nuance of a sentence, and for validating whether a sentence is grammatically correct or not.

By first stripping out all the quality in the sentence, simplifying it into the most basic SVO structure, we can reconstruct the sentence context step by step.

Attempt 1: 我们只有一个红萝卜剩下。 [this feels like "we have only one carrot to leave behind"]

wrong order of 剩下

Attempt 2: 我们只有一个剩下的红萝卜。 [this feels like "we have one leftover carrot (although maybe we have non-leftover carrots)"]

It is a correct sentence, but the meaning sounds like: (in terms of food,) we have nothing but a leftover carrot. No bread, no milk, just a carrot, and it is leftover.

Attempt 3: 我们只有一个剩下着红萝卜。 [maybe this? although it seems peculiar]

Wrong. I guess “剩下” can never be used together with “着” because it is an instant action.

Attempt 4: 我们只剩下一个红萝卜。 [I'm uncertain, it sounds like 剩下 has an agent 我们 here]

Correct sentence.

Attempt 5: 我们剩下的只有一个红萝卜。 [this feels like "what we have leftover has one carrot (although maybe we have non-leftover carrots)"]

It is a correct sentence, but the feeling is not. It can happen after some activity. After the activity, we did some inventory. For example, we went to a picnic with some food. We ate almost everything. After the picnic, there was only one carrot left. You say, after the picnic 我们剩下的只有一个红萝卜。We had nothing else leftover.

---

4 is the best but it can be better: 我们只剩下一 根 红萝卜 了

In Taiwan, you can say 我們(we)只(only)剩(have left)一根(one)胡蘿蔔(carrot). We use 只剩[something] to denote we only have [something] left. In Taiwan, 紅蘿蔔 and 胡蘿蔔 is the same thing.

We only have one carrot left.

As indicated by other answers, the sentence can be translated to 我们只剩下一个红萝卜了.

You may try to forget English when you write Chinese. For this particular context, we may put: 我们就剩一个胡萝卜了。/ (我们)就一个胡萝卜了。/ (我们)只有一个胡萝卜了。/ etc.

PS. Colloquially, 个 is fine. 根 is the formal measure word for 胡萝卜.

My translation: 我们只剩一个胡萝卜了

And your attempts:

Attempt 1: 我们只有一个红萝卜剩下。 [this feels like "we have only one carrot to leave behind"]

Attempt 2: 我们只有一个剩下的红萝卜。 [this feels like "we have one leftover carrot (although maybe we have non-leftover carrots)"]

Attempt 3: 我们只有一个剩下着红萝卜。 [maybe this? although it seems peculiar]

Attempt 4: 我们只剩下一个红萝卜。 [I'm uncertain, it sounds like 剩下 has an agent 我们 here]

Attempt 5: 我们剩下的只有一个红萝卜。 [this feels like "what we have leftover has one carrot (although maybe we have non-leftover carrots)"]

Attempt 2, 4 is better (sounds more natural)

Attempt 1, seems good. (sounds not so natural)

Attempt 3 is wrong. (grammar is wrong, no one would say it like this)

Attempt 5 seems wrong, depends on the context.

她可怜巴巴地向我哭诉，“我们只剩下一根胡萝卜了！”
She plaintively cried, "We only have one carrot left!"

我回答道，“你到底要什么， 那根胡萝卜还是这根棍子？
I replied, "So, what do you want, that carrot or this stick?"

(I need a break from learning Python!)

I think 只有 is more 'we only have', not so much 'we only have blabla left'.

We have only one carrot left.

我们只剩下一个红萝卜了。

I guess you want to focus on the grammar, so the above is the first one that comes to my mind. Notice the 了 at the end that goes hand in hand with 只.

As another example

Now we have only one option left.

Now we are left with only one option.

我们现在只有一个选择了。

For the word choice, you may choose to replace 一个红萝卜 with 一根红萝卜. That's a minor part.