I'd love to help, but I'm afraid I'm not up on 4th edition - my gaming group has decided to stick with 3.5, as what we've seen of 4th edition has left us all uninterested in converting. So, I'll offer up what advice I can, but I'm afraid it will be limited by my own ignorance of the 4E rules.
As the "Challenge of Champions" series progressed, it became less and less important to have one fighter, one wizard, one cleric, and one rogue on the team, as I tried having all spells used in the scenarios cast by using
rings of spell storing, which a member of any class could use. As I understand it, 4E doesn't allow for magic rings until you hit 10th level (I may be misremembering this), so that could be an issue, but is there some sort of "spell storage and release" magic item in 4E? If so, you'd probably want to use that for any specific spellcasting for the individual scenarios. That way, a group of, say, four fighters could compete in the Challenge and still hope to do reasonably well.
As far as writing a "Challenge of Champions" adventure goes, if you're going to keep the same basic format, you'll have 10 scenarios. These usually fall into one of the two following categories:
1. The PCs must get from Point A to Point B, overcoming some sort of obstacle along the way. (And sometimes they have to retrieve one of the PCs while they're at it, who starts the scenario imprisoned somewhere.)
2. The PCs must figure out a puzzle of some sort to allow them to do whatever the scenario goal calls for. Sometimes this is figuring out the command word to a magic item, or deciding which one of multiple exits is the only safe one.
If there's going to be a "unifying theme" (most often involving a "puzzle type" scenario for scenario 10), then it's going to be easier if you first figure out what the last scenario is going to be. For example, one of the earlier Challenges had a treasure hunt for scenario 10, where you had to use the titles of the previous scenarios as scrambled clues to tell you where to go on a grid to find the hidden treasure. Obviously, I first had to come up with the clues (the names of the first 9 scenarios), then build the 9 scenarios around those particular titles. (This isn't as hard as it sounds; sometimes it even makes coming up with the scenario fairly easy. When I needed a scenario to be called "EON PETS," for example, it was pretty easy to figure out this was going to have to involve wolves in some way, as they were undoubtedly mankind's first "pets.")
If you don't want to have a "unifying theme" for your Challenge, then all you really need to do is come up with 10 different scenarios. All I can really suggest as far as scenario-building is to come up with the types of scenarios that your players will enjoy; if your players hate word games, maybe it would be best to stick to the "Point A to Point B" types of scenario for your Challenge. Go through the spell list in the
Player's Handbook and the magic items in the
Dungeon Master's Guide and see if anything jumps out at you as far as creative uses that could propel a scenario's "trick solution." This is often using something in a manner it's not normally used (like getting a spellcaster higher off the ground than normal so that a
rope trick spell will reach high enough - and even then, the
rope trick spell isn't being used for the extradimensional space but rather the vertical climbing rope). Sometimes it's as easy as using a magic item in a non-magic fashion (a cursed
rope of strangling is still a perfectly usable rope, as long as you don't try commanding it to do anything).
In any case, if there are cursed items in 4E (I can't recall having heard one way or the other), don't be afraid to use them in your scenarios as well; sometimes you can build a whole scenario around figuring out which similar-looking magic items are the safe ones and which are the cursed ones.
Hopefully, this will be of some use to you, although I'm afraid all of my advice is necessarily basic due to my own lack of 4E knowledge. If you do manage to come up with a 4E "Challenge of Champions," I'd love to hear how it went. And feel free to ask me any questions you might have, although again my assistance is likely to be more on the broad level rather than dealing with 4E specifics.
Finally, thanks to Mistwell for the kind words and for bringing my attention to this thread.
Johnathan