"intimate time" is correct and can be used in written English.
It is commonly used to refer to a period of time dedicated exclusively to spending time together with a significant other or close friend. For example, "After a long week, we both needed some intimate time together."
"This is an intimate time in a woman's life.
If you had to spend intimate time with Prince Andrew, wouldn't you take a parrot?
We had a very intimate time together, Madame Crazy and I, sleeping curled up next to each other like kittens.
You go to these places, you teach and share this really intimate time with them, and then you never see them again.
Just by stepping onto the reddish dust of the warning track, the fans had made the leap backward into a more intimate time.
The roving, probing, lunging cinematography (by Michael Wadley) turns the movie into a spectacular yet intimate time capsule of urban turbulence and vigor.
The characters, in their thirties, even pressing forty, carry a growing weight of romantic memories — their recollections of people whom they loved and lost (or left) surge forth during intimate times with new lovers.
One of the most intimate times you can spend with someone is when they take their last breaths.
That intimacy when you're nose to nose with your lover those are some of the most intimate times.
The less judgmental we are, the more intimate we can become with our partner, and it's during our most intimate times that we make the most important discoveries about our deepest self.
We are thinking about other women even in apparently intimate times and are perfectly capable of harbouring sexual and romantic desires for other women while being in love with our wives.
