Brown scored one try and created another as Swinton recorded a 37-31 victory over Dewsbury Rams, while Ellison produced an inspirational 60-minute spell in the front row as Oxford beat York City Knights.
Every week each coach in both Kingstone Press Championship competitions is contacted to help produce the awards.
Lions coach Ian Watson said: “James has been very hard to deal with for the last couple of teams that we’ve played.
“With ball in hand he’s been phenomenal.
“Teams are struggling to hold him because he punches holes in defence and gets his arms free for offloads.”
Oxford coach Tony Benson said: “Dave came on after 20 minutes and stayed on for the next hour. He really lifted things in a period where we’ve struggled in the past.
“It was an inspirational session from Dave; he led from the front, he was constantly poking his nose through in the collision and was talking to the team throughout.
“He’s been good for a while, but this was a particularly good display against very tough opposition.”