I have some mixed thoughts on the whole Qur’an/Koran transliteration issue. That is, I’m not certain whether it is, in general, disrespectful to transliterate things in one way instead of another. Most writing systems have multiple conventions for transliteration into English, and often even native speakers of the language disagree on how to transliterate.
In Mandarin, for example, transliteration can either attempt to account for tonality, or ignore it entirely. Some methods mark the tone of each syllable with a number, but this produces VERY hard to read text for the average English speaker. Also, Mandarin has sounds that are difficult for English speakers, because we don’t have them in our phonology, so it sounds to us like it is somewhere between two different letters. Choosing how to transliterate that is pretty arbitrary. In Pinyin, ‘x’ is actually [ɕ], the alveolo-palatal fricative. To English speakers, it sounds kind of a ‘j’, kind of an ‘x’, and kind of like an ‘sh’, and it has, at one time or another, been standard to transliterate it with any of these. In practice, however, it is none of these; it is simply a sound our language doesn’t have at all (as far as I know).
So, Qur’an is difficult for English speakers on a couple of levels. First, the sound being transliterated as either ‘q’ or ‘k’, like [ɕ] in Mandarin above, has no English equivalent; we don’t use the sound at all (for the curious, it’s the voiceless uvular plosive). In addition, ‘q’ and ‘k’ are not meaningfully differentiated in a lot of English dialects (I know in my area, ‘kween’ and ‘queen’ are pronounced the same way (obviously, ‘kween’ is a word I just made up to illustrate the pronunciation of ‘queen’)). Next, the ‘u’ doesn’t do what English speakers expect, but ‘o’ is even worse there because it’s actually IPA [u], which English typically spells ‘oo’. Also, English doesn’t have a symbol to mark glottal stops, so that apostrophe is going to convey no useful information for a lot of people.
Now, all of that said, I don’t think ‘it is difficult’ is a good excuse. I do not know very much about Arabic; everything I explained in the previous paragraph I learned with a 5-minute excursion into Wikipedia. And if native speakers have a generally accepted preference for transliteration, I hold that that is what should be used (even if it is downright confusing to me, see Gaelic).
However, saying that Qur’an is more correct than Koran is shakier territory. The only ‘correct’ spelling is:
القرآن
Anything else is an approximation. There doesn’t seem to be any standard transliteration system into English from Arabic, and the points of contention (the q/k and the u/o) are both debatable, as described above. I do think it is just lazy not to include (and take the time to be educated about) the glottal stop marker, however. So, whether you insist on Qur’an, Kor’an, Qor’an, or Kur’an, please remember the ‘.