Does Harley Quinn ever have children, either with the Joker or with someone else? We see her have them in a dream sequence in the 2016 Suicide Squad film.
In the DC Animated Universe, yes.
While we never learn anything about her actual child/children, we meet Harley's two granddaughters, Delia and Deidre (together referred to as "Dee Dee").
Like their grandmother, they are gymnasts and criminals. They are members of the Jokerz, introduced in Batman Beyond: Return of the Joker.
In Injustice: Gods Among Us Year Two #13, Harley admits to Black Canary that she had a daughter named Lucy, fathered by Joker.
Injustice is a separate universe, which does not necessarily reflect the state of things in the main continuity (whatever it happens to be these days). Yet, I think there was a crossover between some main continuity and Injustice.
In Injustice 2 #2 she even calls the woman who is taking care of her daughter:
While I don't have a vast amount of knowledge from the comics, there is an easter-egg in the Arkham City game that involves this.
When the player first visits the Steel Mill where the Joker (together with Harley) have holed up as their hideout, a crib can be seen in the office they are using to plot:
Around the crib on the floor can be seen positive pregnancy tests:
Spoiler for the rest of the game and the DLC follows:
Once you have completed the game, and the Joker is dead, you can revisit the Steel Mill under solely Harley's control. If you head back to the office, you can find the following scattered around: This would seem to imply that - in the Arkham game universe at least - she doesn't (can't?) have children
I wanted to add in here, along with Harley’s Enchantress vision of kids (specifically, a boy and girl), there are baby onesies in this scene with Joker in the upper corner. One pink, one blue, and also what looks like a black one. Maybe a baby died? Her speech to Diablo about kids would make more sense now.
Own that shit. Own it! What do you think was going to happen? Huh?... What, you were just thinking you can have a happy family and coach little leagues, and make car payments? Normal is a setting on the dryer. People like us, we don’t get normal!
Also worth mentioning, they also took a step away from Harley’s typical red/black colors and did pink/blue (baby colors) for her hair in Suicide Squad.
Yes, Harley had a daughter whom she let her sister raise.
She left the Joker for a year to have said child because she feared that that learning he is a father would lead to a worsening in the Joker's mental state.
Her name is Lucy.
She was referenced to in a comic, where Harley refused to finish fighting Black Canary because Black Canary was pregnant with Green Arrow's child.