java.util.GregorianCalendar is the only subclass (as of 1.4.2). I'd set two calendar objects using your two dates (java.util.Date):
GregorianCalendar c1 = new GregorianCalendar();
GregorianCalendar c2 = new GregorianCalendar();
c1.setTime(dateA);
c2.setTime(dateB);
You can then retrieve the day of the year from those calendar objects as an int:
int d1 = c1.get(Calendar.DAY_OF_YEAR);
int d2 = c2.get(Calendar.DAY_OF_YEAR);
Subtracting one from the other will give you the difference in days between the two dates:
int diff = d2 - d1;
This should work as long as the dates are within the same year. A little extra tweaking should make it work across years. Hope that helps.
java.util.Calendar