It looks like a Kyushu dialect, according to a Google Search. I don't think it's really possible to equate it to any specific dialect of English. Although, in my experience, in Japan most non-standard dialects of Japanese are considered low-class, and are usually associated with the countryside. They could probably all be equally rendered in English using a dialect associated with country folk (like some varieties of Southern U.S. English, for example).
Which makes me wonder: why Cockney? Cockney is a city dialect, isn't it?