Are you saying that the 1929 date is a guess? They normally search a few years on either side of the year given. That application form also has a line for last address if you are not sure of the county. I have had success in the past by giving an estimated year and place. The form states to list all possible dates of death and names under which the certificate may be registered. There is also a toll-free number on the website that you can call and ask about the requirements.
If you don't have an Ancestry subscription as Dick suggested, I understand that the Arkansas Historical Commission has a list of state deaths to about 1946. Maybe you can send an e-mail asking if they can do a lookup for a date. Website ishttp://www.ark-ives.com/http://www.ark-ives.com/.