While I do not know the source, I have heard many times that Gentiles are forbidden from keeping Shabbos and must make sure to violate at least one law of the Shabbos every Shabbos. If this is the case why is it not among the 7 Mitzvos for Bnei Noach? Additionally, are there any other commandments for Gentiles not listed among the 7?
Gemara in Sanhedrin 58b-59a:
ואר"ל עובד כוכבים ששבת חייב מיתה שנא' (בראשית ח, כב) ויום ולילה לא ישבותו
And Reish Lakish said, A non-Jew who observes Shabbos is obligated to be put to death, as it says, (Bereishis 8:22) "Day and night, you shall not rest."
The succeeding Gemara explains that this applies to any day of the week. It is not counted in the Sheva Mitzvos because it is strictly a Kum V'aseh - you must work. The Halacha of setting up courts, which is included, is both Kum V'aseh - do justice - and Shev v'al Ta'aseh - don't pervert justice.
This is a snippet of a larger Gemara (56a-60a) that discusses the Sheva Mitzvos. It lists several others not mentioned in the main seven:
R' Chananya Ben Gamla - Eating blood from a live animal
R' Chidka - Castration
R' Shimon and R' Yose - Magic
R' Yose - Divination
R' Eliezer - Kelayim
R' Dimi amar R' Elazar amar R' Chanina - Bi'ah with a slave who previously had bi'ah with another slave
Mishum R' Yishmael amru - Causing a miscarriage
R' Elazar amar R' Chanina - Unnatural Bi'ah
R' Yochanan - Learning Torah (other than the mitzvos that directly apply to him)
A goy is assumed to be an idolater(R"Eliezer,Gittin 45b and H"Assurot Maachalot 8:11). A goy should only be involved in the sheva mitzvot bnei Noach.
Notice the different dinim between a goy and a ben Noach in H"Melachim 10:10 about tzedekah.
A better question, is what happens when a goy is no longer an idolater. Can such a non-Jew keep Shabbat(as a Jew)? Only rest on Shabbat(like a ger toshav of Krisos 9a)?