With a little modifications a gate closer could be modified on a timer. I personally haven't seen one for sale like that. One issue I do see is that gate closers are usually intended for driveway gates. They definitely would crush any birds in their path. What about adding a pop door next to the...
Close up any openings in the coop with hardware cloth. Is it covered? And does it have an apron? A lot of predators can get through gaps you'd most likely ignore as secure. And most are agile climbers, don't forget to look up. Pics of the coop will help with future advice. Best of luck.