A conventional apology is rooted in the apologizer's fear of unworthiness. Young children, who know their inherent worthiness, rarely apologize except under duress or when emulating adults.
A "positive apology" is possible, however. The thoughts behind it might go like this:
"All Is Well with me and you. Our well-being and worthiness are certainties. I am aware that some of my past actions were out of accord with who and what I know myself to be. And in that awareness, I have more clarity about how I want to interact with you from now on."
In other words, a positive apology is simply an affirmation of Who You Really Are. No shame. No blame.
Children aren't picky about how they express such thoughts. It could be as simple as a hug or "I love you."
Next time you feel like apologizing to your child, speak as if you were expressing only love and appreciation. Remember, your "vibe" matters more than your words.
• See examples in comments below...