A couple of issues:


int main(); should be int main() (no ;)

myDay.printDay() const; should be myDay.printDay();
You can't do this:
cout << myDay.printDay() << endl;

because printDay() does not return anything (it returns void)

Also,

You'll end up with some kind of endless loop/recursion here as you are calling your self inside:
void dayType::printDay() const
{
cout << "The day is: " << dayofweek << endl;
printDay();
}