I would like to take some more coffee is something I could want to state when I am pouring myself a tiny bit of coffee in order to share equally with the others present. I would love to have some more coffee is something I would use if someone else is pouring the coffee. I think both can be fine translations for the Swedish sentence.
It makes the sentence conditional, with the implication of "...if that is possible". There is a politeness imbedded in the statement (actually a request). "I love to have some more coffee", although technically grammatical is an unnatural statement in English. "I want to have some more coffee" is a correct, though more direct and less polite, statement.
The V2 rule (verb coming second in the sentence), which seems to apply in simple sentences except potentially for questions, where it might get moved into first place. Things can get more complicated in a second clause of a compound sentence. (The second place may not be strictly the second word, as the first word might have a modifier or two attached to it, but is what might be characterized as the second functional element of the sentence).