I assume we are talking about the Cartoon Young Justice (which I love!)
So probably the easiest way to do it, is to use the Rogue as a base template (to represent more of the skilled nature of many of the heroes) and then allow people to choose one "X level" spell as an at-will ability (no concentration), or two "X-Y" spells at-will, or a class ability at will, etc. Or some abilities are just permanently on. Then you could allow fighter classes for the martial focused classes. From there we can do some tailoring. Note that these powers are not balanced, nor are they in teh show. If you actually want characters to be somewhat balanced with each other, you will need to adjust levels. Ms Martian might be a 3rd level rogue, while Nightwing is a 10th level rogue/3 fighter....to provide some measure of parity between "normal people" and "meta-humans"
Kid Flash - Haste at will, and maybe allow for the haste action the ability to cast haste again. This allows him to get faster and faster but in a way that's at least requires some build up.
Robin/Nightwing - Rogue with some fighter levels, and several "magic items".
Artemis: Fighter with true strike permanently on.
Beast Boy - Wildshape at will
Aqualad - Permanent Water Breathing, swim speed, control water at-will. Maybe some magic swords to represent the water swords he often uses. Probably some fighter levels.
Superboy - Haste, Stoneskin, Enhance Ability (Strength) all on permanently.
Ms Martian - Polymorph at will, Fly (always on), telekinesis at-will, detect thoughts at-will.
Zatanna - I would probably just stat up as a wizard.