A definition of Putra(a son) from Manu Smriti:
Manu Smriti 9.138. Because a son delivers (trayate) his father from the hell called Put, he was therefore called put-tra (a deliverer from Put) by
the Self-existent (Svayambhu) himself.
In fact,one of of the main reasons why a couple begets children is to have someone to provide them libations of water after they are no more.Now knowing this which parents will purposefully decide against having children? It is for their own good after all.
And,of course then comes the Pitru Runa(the debt that one has to the ancestors).For that too begetting sons are necessary.
Further relevant verses:
Manu Smriti 9.106. Immediately on the birth of his first-born a man is
(called) the father of a son and is freed from the debt to the manes;
that (son), therefore, is worthy (to receive) the whole estate.
Manu Smriti 9.107. That son alone on whom he throws his debt and
through whom he obtains immortality, is begotten for (the fulfilment
of) the law; all the rest they consider the offspring of desire
Manu Smriti 9.137. Through a son he conquers the worlds, through a son’s son he obtains immortality, but through his son’s grandson he gains the world
of the sun.
Does Dharma allow one to consider having a child to be a karmic bandhana and therefore avoid it despite not being in vAnaprastha ?
I don't know of any Scriptures that preach that logic.
Now can he and his wife together decide not to even try for having a child ?
As told above, it is in their benefit only to have one.But as per this Kurma Purana chapter a Grihasta(householder) can be of two kinds: 1)Udaseenas & 2)Sadhakas.
Again Grihastis are of two kinds viz. Udaaseenas and Saadhakaas; the
former Grihastis lead a virtuous life and simultaneously take up
family responsibilities too are Sadhakas; while those who leave away
the Pitruruna, Devaruna, Rishiruna besides leave family, money and
social obligations and remain targetted only at Moksha are Udaseenas.
So,Udaseena is the type of householder who will not want begetting children but i'm not sure how can they compensate for not having paid the 3 debts or what the consequences of following such a path are.
Moreover,the "Udaseena" is more concerned about moksha than anything else.So he is behaving like a Vanaprashti here.But the couple you mentioned in your question are not inclined towards moksha yet.So ,this path is not for them in any case.
Also,a verse from Manu Smriti,discourages that "Udaseena" path by saying:
6.35. When he has paid the three debts, let him apply his mind to (the attainment of) final liberation; he who seeks it without having paid
(his debts) sinks downwards.
However ,this verse applies to a Brahmin.