Of course, just put the center of gravity back to its rear limit and fly slowly. Then all of them will produce positive lift on their tails.
Stability is not produced by a downforce at the tail. The newest book I read which claimed this was from 1911 (I happened to read the 1913 edition). Stability is produced by making the lift per area of the forward parts higher than that of the rear parts. If the lift on the forward wing is high enough, the rear wing can provide stability with a positive lift.
Canards should be the easiest to prove this: Their main wing produces positive lift, and still they can be made to fly stable.
If you are looking for a design which seems to deviate from this basic principle, maybe the Fauvel AV.36 will do:
Fauvel AV.36 in flight (picture by Daniel-Wales-Images)
Charles Fauvel designed several flying wing gliders, of which the AV.36 is the most popular. All of them had positive, natural pitch stability. There is only one wing, and it must produce lift, or the plane couldn't fly, right?
The only way to really do away with this principle is to give up natural longitudinal stability. Weight and balance would be affected such that the center of gravity is behind the neutral point, where the angle-of-attack-dependent lift force acts. This kind of airplane, however, would be very hard to fly manually.