There is a local tattoo artist called Barry K who does a few cover ups and laser removal. He works with people to create a design they like and then only recommends laser treatment on the sections that wouldnt be fully covered by the new design.

Might be worth looking at that as an option.

Alternatively, go to a well known tattoo studio with a good reputation (a guy I know is going to Nikole Lowe's studio down in London to get his done) to see what coverup they could do.