The preposition to can express a possessive relationship.
Where is the key to this lock?
The key that belongs to or belongs with this lock.
In your sentence, to works well because "couples" are entities, as a lock is an entity. The silence is "theirs" to share. It is not an intrinsic characteristic of them.
We use inherent in when referring to intrinsic characteristics of situations more abstract than "couples":
There is risk inherent in any investment.
They shared that comfortable silence inherent in/to couples who no longer need to impress each other.
preposition and verb:
They shared that comfortable silence existing between couples who no longer need to impress each other.
Generally, one says there is silence between two people. And I find it quite odd to say that a silence is inherent, unless you say it is inherent in the relationship between two people, which would give us:
They shared that comfortable silence inherent in a relationship between couples who no longer need to impress each other.
As we say in a relationship here, I would use inherent followed by in due to the phrase "in a relationship".
If the phrase as had been to the relationship or something else with to, I would have used "inherent to [doing some activity].