Those on base Xbox One and PlayStation 4 consoles will not be able to host a co-op session on Dead Island 2's release. Instead, they will have to rely on players with more recent consoles (from the same console family) to be the host.
In a recent blog, developer Dambuster Studios stated that, due to Dead Island 2's graphic requirements, "the host must play on the latest generation console (PlayStation 5/Xbox Series X S) or one of the Generation 8+ consoles (PlayStation 4 Pro/Xbox One X)". The host can then be joined by up to two more players.
As such, those on original PS4 and Xbox One consoles will not be able to host a session on the game's launch. The developer is working on a solution for this, with the plan being that everyone playing Dead Island 2 will eventually be able to host a session, regardless of console. Dambuster has not given a timeframe for this update as yet, merely stating it is planned to come "in the future".