What does this sentence mean? ''I need us to maybe put times aside that I can count on.'' If ''times'' means ''the circumstances and ideas of the present age'' What can he count on?
In the context of that dialogue (Created for Connection: The "Hold Me Tight" Guide for Christian Couples, by Sue Johnson, Kenneth Sanderfer),
putting times aside is about saving time for a special purpose (making love there, so scheduling for that - so she could count on specific time periods, times).
In relation to a schedule or planning, times refers to time slots or time periods, as in
When are a few times you’re available for lunch?
Although in plural form, the question above typically seeks to coordinate schedules for a single lunch appointment.
In contrast, keeping with the times or keeping up with the times refers to staying stylish, fashionable, or modern and is the meaning you referenced in your question. Perhaps ironically, this construct is a bit dated and old fashioned.