Wikipedia has a list of Bible translations in the Swedish language. There are two types of Bibles:
- Official government-sanctioned translations, used by the Lutheran Church of Sweden
- Other translations
The 1917 version that you found is most likely the 1917 års bibelöversättning, which is a government-sanctioned translation. The latest government-sanctioned one is the Bibel 2000. Given that it is used by the Lutheran Church of Sweden, which is the largest denomination in the country, you ought to have an easier time finding this version.
Other translations are most commonly available in the New Testament only, but it looks like the Svenska Folkbibeln (Swedish People's Bible) is the most popular non-government modern translation that contains the entire Bible. Wikipedia has an unsourced claim that this translation was commissioned in response to conservative concerns that the Bibel 2000 was strongly influenced by liberal theology and higher criticism, but I couldn't find anything on my own to confirm this (although I'm limited to English sources since I can't read Swedish).*
It does not appear that a Swedish translation to the New King James Version (NKJV), or English Standard Version (ESV), are available. I suspect that is because they are of interest to English language speakers, but less so to Swedish speakers who would prefer a translation from the original languages to their own language.
*As a personal note, I'll say that it's not worth getting worked up over whether a Bible translation is "conservative" or "liberal"; I personally can't tell unless I really search for differences. Just get a Bible that you can find. If your friend attends a church that uses a certain translation, that's an excellent version to pick up, and means they will read the same words in both services and private study.