Yavor, I looked a little more what I could find here.
I agree these notes are a little contradicting.
Only, I don’t have any books or magazines to hand here and just could compare what is to find in the web. According to Aerofiles there are 3 aircraft that are included in this story – two built by Wiseman and one by Maupin and Lanteri’s “Diamond Aircraft Co.”
Aerofiles offers theses pictures:

1910 Wiseman Biplane with modified 50 hp automobile engine (looks like a V-type)

1911 Wiseman-Noonan Pusher with Hall-Scott engine (I have not a possible model but it looks also like a 8-cylinder V-type)

1910 Black Diamond Pusher with 50 hp Roberts 4LW (a 4-cylinder inline engine)
Though looking very similar, the three-cycle undercarriage of the Diamond Pusher differs to that shown in the picture. And Aerofiles continues the history. After beeing stored away by the NSAM in 1948 it was send back to California in 1998, was restored and now is exhibited in the Hiller Aviation Museum in San Carlos.
The Diamond Pusher story is also told here:
Hiller Aviation & Museum | Events
And several webshots show the Curtiss-type pusher with 3-cycle landing gear in the museum:
1911 Diamond 1 on Flickr - Photo Sharing!
So I think we do have here the second biplane built by Wiseman with financial support from Noonan, that was purchased by Weldon B.Cooke. He repowered the pusher with an 75 hp Roberts engine, that explains the different engine seen in the pictures.
Roberts built inline engines, though the 75 hp is given as a 6-cylinder inline.
Maybe there was another one apart from the 75 hp Roberts 6LW?
The cunfusion might be caused by the connection with Weldon B. Cooke who flew both aircrafts and if not looked closer to these pushers they look very similar.
But I must admit my answer given after a quick search was not quite correct as I didn’t seperated between the two Wiseman biplanes. But maybe the new engine qualifies to name it “Wiseman-Cooke”?
Oh, and not to forget, the different tank installation indicates that the two pictures offered before were not taken on the same day. I thought it could have been ‘cause the airfield does not really look like a pre-war field.
Cheers
Aquilius