I would check with Hamilton Orchards. I found some research they did and it said they thought Boysenberries might be a possible addition to their crops.
I'll ask them next week at Copley or City Hall.
I didn't find them on the sites that give a calendar of local crops.
I would check out the local farmers markets. I remember seeing them as a kid at Lee's farm market in Wayland, but that place is long, long gone. Last year one of the stands at the waltham farm market had a number of unusual berries, but I don't specifically remember boysenberries.