While I tend to like the more morbid ballads, many of which have great visual possibilities (like the Two Sisters turning of a breastbone into a harp, Willie's Lady in protracted labor, False Lamkin and the wicked nurse sticking the baby with pins to lure his mother down to her doom, etc), they may not be appropriate for a children's picture book. Here's a few of suggestions of ones that might work well:

The Mockingbird Lullaby (in DT here) –it's not a story song, but has good visuals. I did a search on Amazon.com and they listed one children's book version, now out-of-print)

The Beggarman or Jolly Beggar is a good rags-to-riches story (look for Child #279 in the DT)

Alison Gross (Child #35, one version in DT here) is great – an ugly witch, beautiful gifts, a magic spell and a rescue with a happy ending.

Chivalrous Shark (may be under copyright) is in the DT here and is gruesomely amusing (or amusingly gruesome?)

The Crafty Farmer's Boy (Child #283, in the DT here) a young boy on his way to market outwits a robber and gains a fortune

Scarborough Fair (The Elfin Knight, Child #2) all sorts of versions here that have fun possibilities for illustrating the impossible tasks.

The Half Hitch – Margaret MacArthur's version of this tale in song is wonderful – lovers in disguise and a happy ending, in the DT here: HALF HITCH

Old Bangum (Child #18) has an evil witch, a fierce wild boar and a brave knight (in some versions…)

I have a marvelous children's book version of Kemp Owen, with the story told by Jane Yolen and illustrated by Dennis Nolan, Called Dove Isabeau - sadly, it's out of print now.