Have Your Child Memorize Anything in Four Simple Steps
And some ideas about what they should memorize.

Children memorize things. It’s what they are good at. Their brains are made for it.
Lean into it.
Helping them memorize stuff is the number one thing you can do for them when they are young (under 8). It’s still important until they reach an age where they can work to memorize things on their own. I’ve found that this is around the age of 10, though every child is different.
What if they are not understanding what they are memorizing?
Who cares? That can come later.
Besides, most adults don’t truly understand what they are reading anyway. Is a child really going to understand all of the theological implications of Psalm 2?
No.
I don’t understand all of the theological implications of Psalm 2.
But if it’s in their head, it is part of their psyche. Their mind will chew on it while they sleep and it will make connections to other memorized facts while they play tag with their friends. All of this work gradually becomes part of the soil of their mind from which creativity can grow.
If they memorize something while young, they will have it with them for the rest of their lives.
Since your children are memorization machines, it is not hard to get them to memorize things. But it will require some work, patience, and above all, consistency.
I spend a little time every night helping them memorize Scripture, right before our regular reading time. (This is a good way for you to be involved directly in their education.) I spend about 5 minutes per child, going over what they have already memorized from the passage and then practicing the next line or two.
Over the past two years, my oldest has memorized 10 Psalms. On just 5 minutes per night. My oldest boy has memorized 7 Psalms. This is completely outside the normal school curriculum, which has its own things to memorize.
Sometimes there are tears and frustration. But just push through. Be consistent. Offer lots of praise.