We have been using a simple, economical method of memorizing Scripture for the last couple of years that I love. I found this idea at Simply Charlotte Mason, a site that is a gold mine for anyone interested in the CM method of homeschooling.
With a few inexpensive supplies, index cards, index card or recipe card box, tab dividers, and something to write with and you're family will be on their way to hiding God's Word in their hearts.
The tab divisions are daily, even and odd, day of the week, and date of the month. Each day, you'll review the current daily verse until it is memorized. Each day you'll also review 3 older verses. Which verse you review will depend on whether the date is an even or odd number, what day of the week it is, and the date. For example today is Wednesday, May 27th. We'll review the daily verse, odd verse, Wednesday verse, and the 27 verse. When the daily verse is memorized, every verse gets bumped back one. Detailed instructions can be found at Simply Charlotte Mason.
Your verse box needn't be a drab addition to your home. Instead of a centerpiece on our table, I have decorated a recipe card box to match my decor. Originally I had covered it with fabric, but have recently covered it with leftover wallpaper that I used when I decorated my barstools. You could also paint or stencil the box, or you could decoupage it with scrapbook paper that is found in a craft store. Use scrapbook embellishments to decoupage over a painted box. Your imagination is your only limit.
If your family hasn't already implemented a system for memorization of Scripture, I highly recommend instituting one. There is no finer way of training up your children in the way they should go. It will never leave them, and God's Word will always be with them even when at times when they might not have access to a Bible.
Faith cometh by hearing and hearing by the word of God. Romans 10:17
Thy word have I hid in my heart, that I might not sin against thee. Psalm 119:11
Thy word is a lamp unto my feet and a light unto my path. Psalm 119:105
The law of God is in his heart, none of his steps shall slide. Psalm 37:31
I delight to do they will, O my God: thy law is within my heart. Psalm 40:8
For the word of God is quick, and powerful, and sharper than any two edged sword, piercing even to the dividing asunder of the soul and spirit, and of the joints and marrow, and is a discerner of the thoughts and intents of the heart. Hebrews 4:12