This question "Why didn't the Clone Troopers have their sex drives removed or suppressed?" mentions that the clones still have their sex drive.
But the clone, Cut Lawquane, mentioned in the text only adopted children, he didn't actually father them. If the clones were able to produce children they might have more cause to abandon the clone wars.
Could the clones reproduce the old fashioned way, or were they deliberately sterilized?
In Legends they could. Venku Skirata was the son of Darman Skirata (aka RC-1136).
Venku Skirata, also known to family and close friends as Kad Skirata, was the Force-sensitive Human male who was the son of the clone commando, RC-1136 a.k.a Darman, and the Jedi Knight Etain Tur-Mukan, and thus a biological nephew of Boba Fett.
Also, Connor Freeman was the son of a clone deserter.
There's nothing in canon indicating any clones had biological children
Canonically, we see at least one child bred directly from a clone trooper.
Maize’s eyes widened. “You fought in the clone wars?”
Sconto let out another belly laugh. “Not quite. My father was a clone.”
It was Karr’s turn to be amazed. “Seriously?”
“If my mother can be believed, and I have no reason to doubt her.”
“But I thought clones didn’t live very long. You must be…” Maize quit before she could speculate.
Sconto didn’t offer her an age, only a wink. “I’m about as old as I look. Either my non-clone blood won the fight, or else I got lucky—and I didn’t inherit their sad, short life span.” If he was telling the truth about his father, then he must be in his late fifties.
Moving into Legends territory, a section cut from the Star Wars: Essential Guide to Warfare (but subsequently republished on StarWars.com) refers to the clone army being fully capable of breeding, but extensively conditioned to not want to do so.
I should also like to address a final point of contention, one I thought had been put to rest during our reviews of the initial Fett prototypes. This, of course, is the question of why these clone units were not engineered to be sterile as per standard procedure.
The answer goes to the heart of why Factor H cannot and should not be eliminated. Two recent human projects – the miners created for Tarshan Ring Excavations and the infiltration squads requested by the Lords of Purala IV — began with trials of sterile clones, as requested by both customers. In both cases the clone prototypes displayed much higher rates of mental instability, poor unit cohesion, an inability to adapt and think creatively, and decreased aggressiveness in battlefield sims. A number of corrective measures were employed — synthetic hormones, rewiring cortical pleasure centers and dietary additives — but all cases improvement was minimal.
It is certainly irregular to recommend that we deliver an army of clone units able to reproduce. But the TRE and Puralan experiments, as well as my experience with humans, tell me that we have no choice if we also want an army that can fight effectively. I propose that we mitigate the situation through the following measures:
Channel the clone units’ normal human impulses for pair-bonding and reproduction into unit cohesion and mission preparation;
Advise the customer to minimize contact with civilians and mainstream human society in crafting the clone units’ daily routines;
Limit knowledge of the clone units’ reproductive capacity to military officials on a strictly need-to-know basis;
and pursue bioengineered contingency planning in the event that a mass emergency reconditioning is required. (Bioengineering could also be useful if further behavioral modification is requested.) This latter option must be pursued with the utmost secrecy due to its possible exploitation by the customer’s enemies.By following this program, I am confident that incidents of clones reproducing will remain minimal, and their impact further minimized through contrafactual public communications by the customer. And in the meantime, we on Kamino will of course continue to try to unlock this puzzle – and the others that come with our work on such a fascinating, confounding species.
