You could put your containers in a baby pool and water from the bottom? Or perhaps something similar.

Find a shady spot for them, or start planting them out! Most of the plants you mentioned should tolerate some cold weather. The sooner you plant them out, the sooner they can develop deep roots and really get growing. And the garden soil won't dry out nearly as fast as your containers. By the way, how deep are your containers? Maybe next year you could try even deeper containers for sowing, so they might not dry out so quickly. Best of luck. I don't have any sprouts yet, so I'm quite jealous here in the cold north.

@Terrene Im may try that

@docmom I used many gallon and 1/2 gallon milk containers and hawaiian punch containers and put about an inch or two of dirt in them.

Not enough dirt in your containers. Three to four inches is recommended so they don't dry out so quickly. Consider this a lesson for next year and plant out as soon as possible. Winter sown sprouts can be planted out while they are very small. Meanwhile, keep watering. Moving into a shaded area will help slow the drying. As the weather warms they may need to be watered more than once a day. If you can not plant out soon you might pot up some of your sprouts.