"The couple cry and laugh together" is a much more typical way to say this in English and yet it was not accepted.
It's more typical in British English specifically. Collective nouns in singular form are generally treated as a singular by verbs in other varieties of English.
I incorrectly translated it as "A couple cries and laughs together." Since Finnish doesn't have articles, is there some way to know that the sentence is talking about the couple rather than a couple?
Sometimes there is, but not here. Without context, either article should be fine.
Would "the couple are crying and laughing together" be a possible translation?
No, because "the couple" is singular. Apart from that, it's fine. Edit: it can be treated as a plural in UK English though, as I have learned some time after posting this.
Thanks - of course!