OK, the bookshelf yields the following candidates:
Rose is the prequel to Bone, exploring Grandma Rose’s earlier life and relationship with her sister. It’s dark in spots, but no more so than the most intense parts of the Bone series.
Amazing Agent Luna is a manga which follows the adventures of an uber-competent, extremely sheltered teenage ninja who has to negotiate the trials and tribulations of high school as part of her cover. There’s some mention of people that were killed in the past, but nothing graphic. I linked to the first issue for the preview, but the first three volumes are available as an omnibus.
Elfquest is pretty much a staple of American fantasy comics, and follows a group of elves as they flee persecution from humans and, in the course of their journey, learn more about themselves and the lost history of their people than they could have imagined. I liked this one a lot when I was younger, but a lot of the more mature material went right over my head. Fortunately, it’s easy to vet before buying, since the creators put up the entire thing online to generate anticipation for the upcoming move.
Destiny’s Hand is about a fantasy story of young girl who rebels against her arranged marriage and throws in her lot with the last honorable pirate captain left on the high seas. When her captain is fatally wounded, it’s up to her and the crew to help his son fulfill his destiny. Some blood and, unfortunately, the writers didn’t get costume design veto, so the main character spends the entire series in hotpants. Preview here.
Polly and the Pirates is more pirate fantasy, but with a bit of a Victorian flavor. Polly is a student at a prim and proper boarding school, and she’s generally content to remain so, until questions of her past – specifically of her dead mother – start cropping up. A twenty-five page preview is available at the publisher’s website.
Beasts of Burden is about the dogs and cats in the quiet community of Burden Hill and their attempts to protect their homes from supernatural encroachment – the collected edition isn’t due out until February or March, IIRC. I love this series, but only cautiously recommend it for a younger reader. As a kid, I remember being a lot more traumatized when reading about animals in danger than people and these are spooky stories with animal ghosts and zombies in a lot of the tales. Definitely needs an adult eye going over it first. Link goes to publisher preview.
Leave It To Chance is set in a more-or-less modern city that’s having issues with some magical elements – goblins living in the sewers and such. Our main character is Chance Falconer, who investigates these disturbances with her pet dragon. You may have to do a little hunting for the first volume, since it’s out of print. I’m also not sure the series was ever properly finished, though I think the third trade does wrap the then-current storyline. Wiki overview.
X-Men: First Class is one I figured I’d toss in here for fluff value, though you don’t seem keen on superhero comics. This series is about the early days of the first five X-Men as students at Xavier’s school and it’s kid friendly – the series has the production values of modern superhero comics without the PG-13 rated material that seems to have become the unfortunate standard. Rather blurry preview for issue #12.