In what way do you believe that the analysis in that page justifies your assertion that:
In order to have positive stability in a convetional layout the tail must pruduce down force
?
Indeed in their summary, they say:
Despite the drawing above, many tail surfaces are normally loaded downward in cruise.
which merely fuels Dani's speculation that some are not. Denker's analysis in the page c172_driver cites is of course correct, and all that is required for stability with an upforce at the tailplane is that an increase in AoA produces a greater percentage lift increase at the tailplane than at the mainplane. For a symmetric aerofoil in a linear range, that usually means a lower AoA at the tailplane than the mainframe (decalage). For other cases, it's the equivalent expressed in terms of gradient of the lift curve rather than AoA itself.
The lift on the tail varies not just with loading, but perhaps more importantly with speed (and configuration), as MFS observes. At low speeds, the mainplane produces a strong nosedown pitching moment, requiring a high downforce from the tailplane to trim it out. So if there is to be a case at which tailplane lift is positive, that would be at the high-speed low-AoA and of the operating envelope, as well as with the C of G at the aft limit. That makes it hard to achieve, because with a low AoA on the mainplane, there is little scope for decalage. But it is nevertheless theoretically possible, and I would have thought it is something that a designer would strive to achieve to reduce drag in cruise. I cannot offer a specific aircraft/loading/speed example though.