Even if I come to Sweden, what can I do for you?
This is the natural first conditional sentence.
Even if I come to Sweden, what could I do for you?
This is possible; you can use 'could' in a first conditional, if trying to be polite, for example.
Even if I come to Sweden, what would I do for you?
Some would say this is wrong and that you should use 'came' with 'would' to make a second conditional. Indeed, it would generally be marked wrong in tests and exams. It might be possible, if 'would' were used for politeness, but I would avoid it to be honest.