Does the deceased ever request a certain casket or coffin?
From my research, it hasn't been widely documented, if it has ever happened. That said, I would expect is has been done. If you have a certain preference for casket vs. coffin, or a specific casket in mind, leave a stipulation in your will similarly to how you would specific a wish to be buried versus cremated. Additionally, make sure your family and heirs know (and agree to) your wish, as often the will is not read or fully read until after the funeral.