I was given the solution. It is enough to force all successive images to be in the same unique domain by adding a common PlotRange :
Manipulate[ Show[point[0, j], PlotRange -> {{-1, 1}, {-1, 1}}], {j, 0, 50, 1}] (See attached notebook)
Maybe this example from "AutoCreate" in the documentation will put you on the right track? You could use Point i.0 Line and hide the locators with Appearance->None
Manipulate[ Graphics[{Line[u]}, PlotRange -> 2], {{u, {{-1, -1}, {1, 1}}}, Locator, LocatorAutoCreate -> True}]
