Some things to think about:
- Does the party have to win all of the challenges? If not, what are the consequences of losing?
- Are the challenges for one character at a time?
- Can they help each other?
These will help you design the difficulty of the encounter in a way that matches your objectives - if every character MUST succeed in ALL challenges, with no help, then you're going to want to make them easier than if the party can match challenges to characters and can get away with losing some of them.
Ideas for skill challenges
STR: Wrestling could be a better fit than fighting. I would allow Athletics rolls instead of straight STR checks. You could also cheat on this one by oiling yourself up to make yourself harder to pin.
DEX: Climbing something (Acrobatics) or evading falling objects (Acrobatics again). You could make this one a race and allow for clever planning of a route to influence the outcome.
CON: Enduring hardship such as frigid water, holding your hand over a candle flame, or holding your breath.
INT: Puzzles are hard to run. One I've used before is the "find the lightest stone" puzzle: Player is given 12 apparently identical stones, but one is hollow. How can they find that stone if they're given a balance scale but only allowed 3 measurements?
One solution: Compare 4 against another 4. If either group is lighter, the stone is in that one. If neither is, then it's in the remaining group of 4. Split the group of 4 into two pairs of stones, then compare the two in the lighter set against one another.
WIS: Detect lies (Insight) might work. You could link this one with the CHA challenge - the player gets conflicting advice on how to influence the target, and must decide which is the truth and which is a lie, with the result granting either Advantage or Disadvantage on the CHA check if used.
CHA: Persuade the judges that they're fit to be knights. Or deceive them, if they're not really fit.