So, fine with me is the standard way to say it.
But fine by me is ok, and dictionaries confirm that. The only mention that it should not be used is here: https://english.stackexchange.com/a/37205/19577
- But what is the background of fine by me? Is it rude/redneck/chav/kid/archaic/odd ?
- What would be an impression about the speaker, when the person is using fine by me?
- Can you use it in business correspondence ?