Ένα παλτό, a coat would seem a better translation than one coat.
It could mean "they only have one coat to share between them". There is no distinction in Greek, only context or spoken emphasis could make that clear.
yes, thinking about it, if they each had a coat you would say "They have coats" so maybe the one coat is better. However to mark "a coat" as incorrect is a little harsh.
I thought you got the English sentence with "one coat" to translate, so there could be no distinction in Greek...