We are inclined to say kaddish on the yahrzeit of a very dear friend who was not Jewish, just as we would for a relative. Is there a reason not to? I am also interested to hear reasons why this is a good idea. Would it make more sense to say kaddish on this person's Hebrew yahrzeit or on the anniversary date on the secular calendar?
I have been told by a Rabbi whom I greatly respect that he has permitted geirim, along with the Jewish son of a non-Jewish father and a Jewish mother, to say Kaddish for their non-Jewish parent(s).
I believe that much of his reasoning was based on Kibbud Av v'Em (which continues to apply to one's non-Jewish parents even after conversion where one is considered as if born anew for other halachic purposes) and because of "Deracheha Darchei Noam" -- the ways of the Torah are pleasantness and the child -- at least one asking the question -- would be distressed if told that they shouldn't say Kaddish for their parent(s).
This seems to me a very different question; one doesn't generally hear of saying Kaddish for a non-related friend (unless they've adopted you!), Jewish or non-Jewish. So I think a consultation with your local Orthodox rabbi is in order. I do think it's safe to say that, if you're choosing a Jewish text like Kaddish, you should use the person's Hebrew yahrzeit.
OTOH, the best alternative may simply be to pick other texts from Tehillim or Tanach that seem applicable but that don't need to be said before a minyan but can be read at any time, and say them in memory of your friend, along with a discussion of your friend's good traits if this is done in conjunction with some other memorial for your friend. If that memorial is done on the English anniversary of death, it wouldn't be a problem in this case.
Also, I (who am not a rabbi, BTW) see no problem in lighting a "ner neshama" (yahrzheit candle) for your friend; that again, should presumably be done on the Hebrew yahrzheit.