The old (pre-S8) comics do mention a Japanese Slayer who was turned a couple of hundred years ago; the Council hushed it up as a big scandal and struck her name from the records. Lots of angst because Buffy met her and Giles refused to explain who she was, but it turned out that Spike knew her from the old days (she was turned by the Master, in fact).
So according to a deuterocanonical source at least, turning Slayers is possible, but very, very rare.
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So according to a deuterocanonical source at least, turning Slayers is possible, but very, very rare.