Short answer: No. "Some day" refers to the future.
I think most English speakers would say that (c) is just wrong. It doesn't make sense, precisely because it breaks the "future" rule of the idiom.
(a) and (b) are acceptable, but that's because they are not really using the idiom, they just looks like the idiom. You're pulling two words out of the middle of a sentence that match an idiom, but it's not really being used the same way. If that's not clear, consider the phrase, "Something came up." This is a common idiom that means, "some event happened or is expected to happen that interferes with previous plans". Like, "I'm sorry, I was planning to attend your party, but something came up." Now consider the sentence, "We forced air in to the bottom of the well, and something came up the pipe." That includes the words "something came up", but clearly we are not using those words in the idiomatic sense. Here we mean them literally, and it is just a coincidence that they look like the idiom. Same thing with sentences (a) and (b). You're not saying, "I saw him some day" in the same sense that you would say "I will see him again some day", and then clarifying that that day was last month. Rather, you literally mean that there was a particular day last month, some day, when you saw him. Similarly for (a).
As JR says, (a) sounds awkward because it looks too close to the idiom, and thus is confusing. I think most English speakers would say "some time around 1900".