Magic is a bit different when performing for children, especially card tricks. They often aren't able to remember or recognize the symbols on the cards and thus don't have the greatest reaction.
Generally, kids 6 and up can remember the names and values of the cards.
The biggest issue for me has been they have very short attention spans. Your tricks need to keep them engaged. If you absolutely have to do something with basic cards, do something quick and visual like a backpalm, color change, or that vomiting card thing.
I'm going to disagree... a bit. I think those types of effects are good at grabbing their attention, but not keeping their attention. My invisible deck routine involves a beachball and music to select the card one characteristic (black/red, hearts/diamonds, face/number, value of card) at a time. My card to nested boxes routine involves a selection, tearing a card, vanishing it from the deck and having it reappear in a bunch of nested boxes. I've done Dan Harlan's Hovercard very slowly with a story for astonished kids.
Again, it is tricks with cards, not card tricks (e.g. gambling demonstrations, sandwich effects, ace productions, etc.).
One good one that tends to work if performed correctly only needs a balled up tissue and a volunteer. You call one kid up and impossibly vanish the tissue in front of him. However, the rest of the audience can see that you just threw it over his head. I tend to not like tricks that work at an audience member's expense but this trick can work in the right context and I've heard some people say they only perform it if there's one kid who's being obnoxious and it's clearly bugging the other kids.
Don't listen to the people who say to bring the obnoxious kid on stage and embarrass them. It doesn't work and you look like a bully. The routine is Slydini's Paper Balls Over the Head and when done right can be wonderfully amusing. The presentation should be fun and playful. You are giving one spectator an amazing experience of seeing magic close up while giving the audience the magician's perspective.
Also, the one problem with doing this effect for kids is that they will yell out what is happening to the spectator on stage.
I highly recommend learning a sponge ball/bunny routine if you're going to perform for kids as it's somewhat easy to learn and kids love it. Plus there are hundreds of possibilities for patter using them.
A sponge bunny routine has a great internal story to it, which is part of why it works.
The coloring book trick is also a classic of children's magic and they love it, because the most common presentation of it uses the entire audience as a volunteer in a way as they all imagine pictures and throw their colors into the book. If you're able to pick up multiple new props and tricks, buy tricks that focus on comedy and audience participation.
I think the coloring book is well suited to those kids age 5 and under. I've never seen a routine that I find interesting, including Silly Billy's routine.
If you're able to pick up multiple new props and tricks, buy tricks that focus on comedy and audience participation.
As I said earlier, kids have very short attention spans. This is why most kid's shows are very bright, comical, and involve many volunteers. It keeps them from getting bored.
Although a lot of this is the "conventional wisdom" spouted by cookie cutter kids magicians, I tend to mostly disagree. A children's magic show, like any magic show, needs to have a texture to it. Merely focusing on the level of interaction (how loud and often the kids scream somthing) rather than the types of interaction and the variety of the effects and presentations makes the show more like a clown act than doing magic. The bright props aren't necessary, the multiple volunteers isn't necessary, the sight gags, the look-don't-see gags and the bumbling magician act aren't necessary.
What is necessary is strong magic, a strong presentation and an engaging character.
This is why story and patter is very important for kids magic. You can't take the Blaine approach of just "watch this cool thing" and perform the trick. You have to give some sort of story or personality to the props so that they want to keep watching.
This is where you almost nailed it. I say almost, because props can't have personality. Only magicians can have personality.
Having a story isn't enough. You need to have an engaging story or presentation. Pretty much every story or presentation I use could stand on its own and be interesting without the magic. Now, everything shouldn't be a story. There is a place (although it is limited) for other ways of presenting magic, including narrating the adventures of the props.
As I said above, shows need to have texture. That means effects use different props, show different effects (i.e. everything doesn't vanish and then reappear), have different presentations, have different pacing, have different tones ranging from silly to serious and have different types of interactions.