When I don’t want oral argument or don’t think it is necessary, my standard operating procedure has been to (1) put nothing regarding oral argument on the front cover of my brief, and (2) include a Statement Regarding Oral Argument in the brief explaining why it has not been requested but adding a statement that, if the Court desires oral argument, then Appellant (or Appellee) would like the opportunity to appear and present argument.
I learned today that the clerks at the Dallas Court of Appeals would like something on the front of the brief regardless of whether you are requesting oral argument. So, in the scenario above, I would (1) put something like this on the front cover: “Oral Argument Not Requested Unless Requested by Appellee and/or the Court,” and (2) include the Statement Regarding Oral Argument in the brief as usual.
This will make the clerk’s office happy because they won’t have to dig through your brief to determine whether or not a motion to allow argument is necessary. It should also alleviate the need to ever file such a motion. A win-win for everyone!