Not sure what a coconut plant is. Is it a palm? Have you fed it? Is it in the shade or direct sun?

coconuts like hot weather. Hot sun and sandy soil, preferably lots of water. Their roots like to spread, so they wont do extremely well in pots, unless you have a bonsai. Remember coconuts are tropical plants, most grown in tropics of asia. We in India only grow them on the coast. Only here you would get fruits(coconuts).
So dont be surprised if it doesnt survive outside in zone 6.
Hope this helps,
Vaishali