But the theory that two masses always attract hasn't necessarily been disproved.
Just from the scenario outlined, there are a number of possible resolutions to the problem that might preserve the theory of gravity inviolate. Perhaps the object that is repelled does not in fact have mass, but has what we might call anti-mass. Perhaps there is some bizarre warping of spacetime around or between the masses causing attraction to behave as if it were repulsion. A creative thinker sufficiently familiar with physics could postulate a number of such resolutions
Each potential solution, of course, would eventually have to accumulate theoretical and experimental justification. But one implication of the Quine-Duhem thesis is that it is perfectly possible that, given sufficient brainpower, one could come up with a solution that preserves gravitation given nearly any experimental results. Which is the theoretical problem with falsifiabilism; one can, if one really tries, cling to nearly any theory if one adopts other postulations that are sufficiently convoluted. Think of the way that geocentrists responded to greater astronomic information by adding more and more epicycles to their model.
Though both have problems in their work, Thomas Kuhn comes closer to describing the way science actually works than Karl Popper.
However you can disprove a theory quite easily just by finding one case that doesn't fit with the theoretical predictions.
I'd recommend taking a class or two on the philosophy of science. As it turns out, this just isn't true.
A theory is not, generally speaking, a single predictive proposition. It is a set of propositions which, when taken together, imply a single prediction. Discovering that the prediction fails does not tell you which of the propositions is incorrect. It is almost certainly impossible to isolate the incorrect proposition experimentally.
This principle is known in the philosophy of science as the Quine-Duhem thesis. The underlying logic has been found to be quite sound.
And it coheres well with our normal intuitions about how science is to be done. If, for instance, we were to find a heavier-than-air object that falls up from a state of rest, we would not scrap the entire theory of gravity. We would realize that this is a special case and try to figure out what the correct way to modify it would be.
If you want to put yourself on the map, publish your own map.