In short: yes.
It can happen by happy accident or it can be part of a careful breeding program. When looking for a new family dog, seek out a dog who adores your children. A-D-O-R-E-S! Goes all ears-back, tail-waggy, melt-in-your-hands squiggly for them.
Behaviors are details; temperament is what you are looking for. Temperament is a pup's inborn, innate, in their genes response to things. Sure, temperament can be worked on and worked with but when it comes to a dog who lives with kids, select one who is already completely over-the-moon about the idea.
Below see the clip of the pup pictured above. She saw the children and insisted on greeting them. When they reached toward her gently she went belly-up, tail-wagging; completely blissed-out at the entire idea and stayed that way until they had to leave over five minutes later.
Now this is a dog I would put into a home with children without hesitation and, I am betting, with no regrets ever. Want to learn more about dogs and children, check out the links at the bottom of this page:
And here she is in live action:
by Sarah Wilson