I have the privilege of doing Assemblies every two weeks with Hawkesdown House School in Kensington. Here are some rules of thumb:
1. Make it interactive. On an Assembly on the topic of Lent, I had five children come up to the front and hold sweets in their hands - which they were NOT allowed to eat - while I told the story of Jesus in the wilderness. The children then talked about whether they were tempted to eat their sweets, how they resisted temptation, and so on. The fact that "everyone was watching" was listed as one thing that helped them resist. This could be an interesting jumping-off point for a longer discussion about sin. Unfortunately, Hawkesdown assemblies are only 10 minutes and include children as young as 3, so I could only briefly touch on the point ("interesting - I wonder how Jesus managed in the desert when there was NOBODY watching!") before finishing up.
For my Pentecost assembly tomorrow, I'm going to ask them how to say "God loves you" in different languages - there's a large international contingent at that school, plus language education from an early age, so I should get a fair number of responses (I'm going to bring a crib sheet, though, just in case). We're going to practice saying "God loves you" in each language, all together, before everyone chooses their favourite and we say it together in ALL the languages to finish.
2. Give it a visual focus. A puppet, a picture (as big as you can make it - at least A3 size),a storytelling doll (they're available for several different stories, not just Easter), a feltboard for Beulah Land storytelling, an icon, a banner - there are many ways to do this. But a visual focus engages children as well as expanding their vocabulary of Christian imagery.
3. Include time for quiet reflection. I personally find this scary. I'm more comfortable with having my time with children be active and dynamic - the kids talking, singing, laughing, busily making stuff. I find it hard to step back and say "now we're going to do nothing" and trust that it will be meaningful. But it will be. Introduce it slowly - start by encouraging them to sit comfortably (maybe with their hands on their knees, palms facing up, in a meditation pose) and close their eyes, to clear their minds and focus on listening to God. Give this time a clear beginning and ending - lighting and extinguishing a candle, perhaps, or hitting a triangle to start and finish the prayer time. At first, try for 30 seconds of quiet, then work your way up to a minute or two. You can close with a communal prayer, such as the Lord's Prayer. I use "keep us, O Lord, as the apple of your eye. Hide us under the shadow of your wings" (Psalm 17:8).
4. Don't be afraid of a formula. You don't need to re-invent the wheel every time. As long as you do it well, there's nothing wrong with "story, discussion/activity, quiet reflection" as a consistent structure to your assembly. Kids are a lot more comfortable with routine than adults are, and as long as the content is engaging, they won't get bored.