Are there any restrictions? You just can't have the Big 7? Nobody who was a member when the League disbanded? I actually think that Dark COIE was a missed oportunity of wasting time with the new PC new versions of the classic heroes instead of assembling a team worthy of carrying on the League's proud tradition.
The JLI could be a good place to start from. I'd go with:
Captain Atom - Leader (The Leadership is the trickiest part in this list. Most of the League's traditional leaders are in the Big 7 - Supes, Bats, Diana, Hal, J'onn, etc..., or even were part of the League when it disbanded - Canary and Ollie, or are in the Titans - Dick and Donna. Captain Atom is the one leader I can think of that is not in that group. Plus, it's be an awsome opportunity to bring him back to the spotçight in a strong way.)
Blue Beetle - Second in command. Tech.
Booster Gold - Time traveling warrior.
Maxima - Female powerhouse.
Faust - Mystical expertise. (Sebastian Faust. Normally, Zatanna is my go to mystical expert, however, if I'm not mistaken, she was part of the team that was "killed" in Dark COIE.)
Vixen - Linked with the animal kingdom.
Dr, Light - Scientific expertise and mistress of light. (There are literally dozens of Green Lantern I could use here, however, Kimyo has a similar powerset, plus the scientific knowhow and the stong personality that makes her more insteresting.)
The Captain - Powerhouse. (Shazam, alongside Captain Atom himself and Maxima provide the team with just about enough physical power to be worthy of being a Justice League.)
I guess the Atom (Ray Palmer), Steel (John Henry Irons), Plastic Man and Mera would also be around quite a lot.
Peace