I definitely would not put them directly into the sun. My coleus seedlings in the garden usually are found in the shade of the 'mother' plant. If you put them in the sun in that coarse soil, they'll dry out very quickly and it may kill them.
But the color of the seedlings in your picture isn't very green, so possibly they need a bit more light. Can you move them towards the light without putting them in direct sun? Or maybe just give them an hour or two of morning sun each day to warm them up?
After you transplant them, maybe try moving some of them gradually towards more light and see if they change color or start growing. Are they staying fairly warm at night? I'm a bit south of you in Sarasota, and our nights have been cool-ish for the last week. Tonight is the first time I've had the a/c on in over a week. The cool nights may have something to do with the slow growth you're seeing, too.
