Can Skyfield calculate the apparent diameter of a planet, the Sun or Moon?
Something along the lines of:
place.at(utc).observe(moon).apparent().angular_diameter
You can work out the apparent diameter if you know the object's radius, with simple trigonometry:
from numpy import arcsin
MOON_RADIUS = 1737.1 # km
appdiam = 360 / pi * arcsin(MOON_RADIUS / place.at(utc).observe(moon).distance().km)