1)The day was completely fun.
2)The day was complete fun.
I think the first one is correct and second one will be acceptable if a is added before complete.
Like Tdol, I don't find these to be very natural. However, it's possible that either might be heard in informal conversation, although I don't know which would be more likely.
The second one is definitely not improved by the addition of "a", to my mind it would become incorrect.
not a teacher