Since preschool children are just beginning to develop a world view, focus Scripture memory on concepts that will help them develop a biblical world view about themselves and the world around them.
Some Bible verses appropriate for the preschool age level:

While entire verses may be too long for this age group, these parts of the following verses could be quite appropriate.
“God created the heavens and the earth.” (Gen. 1:1)
“I am fearfully and wonderfully made.” (Ps. 139:14)
“Believe in the Lord Jesus.” (Acts 16:31)
“The Lord is good to all.” (Ps. 145:9)
“Love the Lord your God.” (Matt. 22:37)
“He cares for you.” (1 Pet. 5:7)
“Children, obey your parents.” (Eph. 6:1)
“Love one another.” (Jn. 13:34)
Key to Choosing Scripture Memory for Preschoolers
Understanding the age level being taught is so important in teaching, even affecting Scripture memorization. If you teach preschoolers, take time to gain a better understanding of this developmental stage. Training Tool: Early Childhood Age Level Characteristics Download
Also check out the Scripture Memorization Discipleship Guide which encourages us to keep memorizing efforts age appropriate. You’ll find a page that zeros in on characteristics of preschoolers that affect Scripture memory. It also includes the above suggestions for verses. The resource looks at other ages groups as well as benefits and means of memorizing.

Excellent advise. I have 9 grandchildren. I hope to be busy with them
Praise God that you see your role as a grandmother to help disciple your grandchildren. Scripture memorization is a great way to lay a good foundation. — Thy word have I hid in mine heart, that I might not sin against thee. (Ps. 119:11)