You might get this naturally, if the takes you longer than 28 days. Note: Even with the 1.04 patch installed, the 28 day timer seems to be glitched. The easiest way to get this though is to do as follows:
Make sure you have the 1.04 patch installed.
Load Dead Island and get to an autosave.
Quit to the XMB.
Go to "Settings" => "Date and Time Settings" and change the date so it's a month ahead.
Load Dead Island and it should unlock on the main menu.
Terminator has some theories as to why this trophy sometimes glitches:
1: You need to play for 28 consecutive days.
2: All 28 days must be in the same month, not spread out over several.
3: It's a combination of the above. There's also the possibility that the DLC screws up the timer somehow but I can't prove it.
When this glitched on me I decided to play for an additional 3 days but it still didn't pop, nor did it after advancing the system clock 1 month. In the end I had to move the clock forward 2 or 3 months before the trophy actually popped. I also had to turn off the auto clock sync option and stay signed out of PSN for the clock trick to work.