I am a convert to Judaism; my non-Jewish family is supportive to my Jewish lifestyle as well as interested in Jewish practices. My sister is a strong Christian believer; after experiencing some Shabbatot with my Jewish friends, she started celebrating a festive dinner on Friday evening with her own family - being aware, that what she is doing is only adapting some customs and not the real thing. But however, she is interested and open. She would like to learn about candlelighting and laws of Taharat Hamishpachah. May I teach her some basic laws? May I as well give her a small booklet with teachings of Rav Nachman of Breslav, dealing with the Mitzva of joy and trust in the Almighty? I do not want to transgress the prohibition of teaching Torah to a Non-Jew.
You should not teach your sister the laws of Mitzvot that do not relate to her- like Shabbat or Taharat Hamishpacha. Joy is not in itself a Mitzva except on Festivals. If you want to persuade your sister to be happy and trust in the Creator- that's fine, but since she is a devout Christian, you should recognize that her concept of G-d differs fundamentally from yours. Your emphasis should be on the seven Noachide commandments and on those actions and character traits that universally define a good human being, be he a Jew or a non-Jew.