Water less. Grapes only need water about every two weeks during a typical growing season. Concord grapes grown in New England may receive enough rain water that they never need to be irrigated. Too much water slows ripening and causes yellow leaves.
Prune and stake vines. Concord grape vines have a drooping habit. If left to their own devices, they'll soon become an overgrown tangle of vines, and they won't ripen well. Train the vines high on your trellis and allow them to hang downward. In the early spring, prune back any vines and leaves, except the main branches, with hand pruning shears.
Harvest later. The main reason Concord grapes aren't sweet enough is because you've picked them too early. Concord grapes turn dark purple weeks before they're actually ripe. Taste them to determine if they are sweet enough. If not, let them ripen for a few more weeks.