On top of JohanC's answer, I personally prefer this way:
import matplotlib.pyplot as plt
box = plt.boxplot([[1,5,6,7,6,10],[1,4,5,5,6,10]],patch_artist=True)
widths = [1,3]
styles = ['*','D']
for n,f in enumerate(box['fliers']):
f.set(markeredgewidth=widths[n],marker=styles[n])
It will give you the results below: