Forget about the cotyledons, their only purpose is to protect the growing tip of the plant as it pushes up through the soil.
They then peel back to expose the first true leaves to light and start the life cycle off.
The cotyledons usually die within 2 weeks and this is normal. They are not required to make the plant grow or to be healthy.
In other words, you have nothing to worry about, the cotyledons are doing exactly what they are supposed to do.
However, by starting your seeds in such small cups and not even filled right up, you are already cramping the root system, which can stunt growth rather quickly.
Black plastic pots about 4 inches across and 5 inches deep are almost ideal for seedlings and provide enough room for three weeks of development. These cups, onl;y half filled with soil are really only adequate for 4-5 days of growth.
Good quality black plastic pots can be washed between cycles and will last for years if looked after properly.
Hope this helps, Organoman.