Our Sunbeam teacher at the beginning of the year made scripture handbags for all the sunbeams in our primary.
She's great with a sewing machine.
She also bought little hardbound Book of Mormons and inserted them.

The handbags were made of canvas but the print on the fabric for each one is different so each one is truly unique.
The bags are small.only big enough to keep the Book of Mormon inside.
The sunbeams have been binging their scriptures EVERY Sunday.

Also, whenever I have sharing time, I make sure to use the scriptures a few times so that the kids see that it's helpful to bring them.
In the Junior Primary, it takes awhile when we read a scripture (opening the book, finding the right page etc) but now they have one reason why they should bring them.