Two psalms that kids should memorize are Psalm 91 and psalm 121.
These are two protecting psalms and psalm 91 especially has a great reputation for saving people in and out of difficulties. This doesn't mean psalm 121 is a slouch. It has its own particular promises which I will get to. And it is easy for a child under 4 to memorize.
1 He that dwelleth in the secret place of the most High shall abide under the shadow of the Almighty.
2 I will say of the LORD, He is my refuge and my fortress: my God; in him will I trust.
3 Surely he shall deliver thee from the snare of the fowler, and from the noisome pestilence.
4 He shall cover thee with his feathers, and under his wings shalt thou trust: his truth shall be thy shield and buckler.
5 Thou shalt not be afraid for the terror by night; nor for the arrow that flieth by day;
6 Nor for the pestilence that walketh in darkness; nor for the destruction that wasteth at noonday.
7 A thousand shall fall at thy side, and ten thousand at thy right hand; but it shall not come nigh thee.
8 Only with thine eyes shalt thou behold and see the reward of the wicked.
9 Because thou hast made the LORD, which is my refuge, even the most High, thy habitation;
10 There shall no evil befall thee, neither shall any plague come nigh thy dwelling.
11 For he shall give his angels charge over thee, to keep thee in all thy ways.
12 They shall bear thee up in their hands, lest thou dash thy foot against a stone.
13 Thou shalt tread upon the lion and adder: the young lion and the dragon shalt thou trample under feet.
14 Because he hath set his love upon me, therefore will I deliver him: I will set him on high, because he hath known my name.
15 He shall call upon me, and I will answer him: I will be with him in trouble; I will deliver him, and honour him.
16 With long life will I satisfy him, and shew him my salvation.
There are many promises in Psalm 91, more than I will go into right now.
And I've already posted about this on my blog and in my book Blogging the Psalms. But for a quick refresher, consider verses 5 and 6. Those who dwell in the secret place of the Most High God are promised safety from evils that come in the night, from swift sudden deadly situations in the day, from plagues, and mass occult infections, and from any kind of destruction in the middle of the day. Those who have anxiety or nameless dread would do well to meditate on this psalm. Verse 3 promises to preserve the one who lives focused on and rooted in God from traps, snares, tricks, and other sneaky bait set by evil predatory people, and it promises freedom from pestilences everywhere. In the Eastern Text, the phrase translated in the KJV as "noisome pestilence" is different and is "conspiratorial gossip." So, if you want to memorize and believe in that version, go for it!
1 (A Song of degrees.) I will lift up mine eyes unto the hills, from whence cometh my help.
2 My help cometh from the LORD, which made heaven and earth.
3 He will not suffer thy foot to be moved: he that keepeth thee will not slumber.
4 Behold, he that keepeth Israel shall neither slumber nor sleep.
5 The LORD is thy keeper: the LORD is thy shade upon thy right hand.
6 The sun shall not smite thee by day, nor the moon by night.
7 The LORD shall preserve thee from all evil: he shall preserve thy soul.
8 The LORD shall preserve thy going out and thy coming in from this time forth, and even for evermore.
Psalm 121 takes a more cosmic view of the universal salvation of God. Look at verse 6. We are promised that the sun will not smite us by day nor the moon by night. This might be a reference to when the Israelites travelled from Egypt and a cloud overshadowed them in the day to protect them from the sun's heat while a pillar of light lit their way at night. Like the Israelites, who were baptized with the same baptism as we are, we also are protected in Christ. But on a purely speculative level, the psalm promises that --should the sun ever go supernova, or should the moon cause all kinds of moon-caused trouble (let's say tidal waves going berserk) the child of God will be protected because the Lord made heaven and earth. Yahweh is not like the Egyptian Gods who only supposedly ruled one area -- rivers, seas, livestock, flies, etc, the sun or the moon. The God of the Israelites ruled over everything in heaven and in the earth.
Moreover, He is able to preserve our soul, spirit, mind and body. He goes before us and after us for all time.