The best policy is to go with nature and plant some trees that like these conditions. The first choice would be alder, a native tree that thrives in heavy wet soil. You could plant these about two metres apart but randomised, not in rows. Mix in a few willows to give bark colour, such as Salix alba ‘Vitellina’. And if you want to add a touch of the exotic, try a swamp cypress, Taxodium distichum.
Control weeds in the early years to get these trees going and after that you will have little or nothing to do with this area which will become a feature in itself with lots of wildlife.