说服: shuìfú vs. shuōfú
In recent years, Mainland Chinese have officially adopted shuōfú across the board. If you only wish to be understood and/or conform to current official standards, a sufficient answer is: just use the shuōfú pronunciation. Everyone will understand what you mean regardless of whether they agree with it.



For a more academic answer: Strictly speaking, shuìfú is the correct pronunciation. This isn't a Taiwanese thing except in that it has been preserved in Taiwan (older mainlanders would have known it too).

The character 說 is an exemplary case of a multiple meaning character with multiple pronunciations. These meanings are not historically interchangeable. Focusing on the relevant definitions at hand:


shuō means "to explain, to tell".
shuì means "to persuade, to convince".


The meaning of 说服 is clearly derived from the latter usage. Therefore, it is correctly pronounced shuìfú. It is still listed as such in many dictionaries. Other examples of the shuì pronunciation being maintained for this usage are 說客, "a lobbyist; someone trying to sell an idea" and 遊說, "to lobby, to persuade."




Ultimately however, languages are living, changing things. It is quite alright to use shuōfú as the pronunciation even if some people would find it as being "wrong". They all understand what you mean anyway.



Note: There's a contention that shuōfú is the correct pronunciation. The argument is that shuì means to persuade, but that, supposedly, 说服 means to "persuade with reason". It is claimed that this means shuō, "to explain", fits the word's overall meaning better than shuì, "to persuade".

I don't find this convincing at all, but that's an alternative angle.