Tea Olive(Osmanthus fragrans) can be difficult to root, as are 2 other species commonly grown, O. heterophyllus(Holly leaf olive) & O. americanus(Wild olive or Devilwood). You would probably have best succes with softwood cuttings taken in July-Sept. and placed in a bark fines/sand mixture that is kept constantly moist. It may take several months for the cuttings to root. They can also be propagated by seed, but it is a much slower process, as it usually takes 2 years for the seed to germinate. Allow the seed pods(drupes) to dry on the tree, then collect and plant immediately. The fruit, although dark in color, is usually totally consumed by birds and you will probably find seedlings under every tree in your landscape in coming years. I don't grow O. fragrans, as it is semi-hardy(foliage) in Zone 7, but I do have the other 2 mentioned above and I am constantly pulling up O. americanus seedlings all over the garden. My O. heterophyllus are cultivars, 'Variegatus' & 'Goshiki', neither which have ever bloomed, even though some are more than 20 years old.
Good luck with your efforts!
Rb

Here is a link that might be useful: Osmanthus fragrans