No translations with "the" seem to be accepted here. However, they are for other sentences in this section.
"I don't have the child" and "I don't have a child" are, indeed, very different sentences, so it wouldn't surprise me if they had different Swahili translations, but if that were the case, I might question the broad acceptance of definite articles for other sentences in this section. Is there something unique about "children," should "the" be ok here, or is it the "the's" elsewhere that are questionable?
This sentence could be used for both English sentences, so it should accept "the" just like the other sentences with "the".
If you really need to indicate that you're talking about a specific child, you can use a demonstrative that's very close in meaning to "the": Sina mtoto huyo "I do not have that (aforementioned) child." And if you really wanted to make sure it's interpreted as indefinite, you could say Sina mtoto yeyote "I don't have any child."