Actually, the Embassy web site states that Taiwanese nationals can travel visa free for short stays within Schengen.
I´d really recommend Denmark in that case. We just had to fill in two short forms, send a few copies of documents (birth certificate, something that states that you are free to marry, proof of address and something else that I forgot) about three or four weeks later we got a letter stating that we can come to the register office on any given Monday at 9 o'clock.
We had to bring the originals of the copies we had sent and ID, along with a fee of something like 75 Euro.
After registering our intention to marry on Monday, we had to 'reside' in that little town until Friday and prove that by bringing a receipt from the hotel we had checked into. On Friday morning all the weddings took place.
We just took that week in Denmark as our honeymoon and in the end we had paid much less for travelling and fees than we would have in Germany.
Otherwise she needs a visa for marriage in Germany:
German Institute Taipei - national visa for marriage in germany
There is a requirement of basic German - I don´t know whether that would be waived if she was to marry a non-German in Germany.
Could also be worth calling the Embassy´s consular section to check the requirements for your specific situation.
There are even agencies to arrange everything nowadays, even without the week-long residency as it seems:
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