Charging a black hole?

There is a limit on how much charge a black hole may have: http://en.wikipedia.org/wiki/Extremal_black_hole

In general, rotating, charged black holes is described by a Kerr-Newman metric.

Intuitively, eventually the Coulumb repulsion is enough that a charged particle which does not contribute more mass than charge will be repelled.

The Coulomb repulsion of the charged black hole does not prevent the charged black hole from acquiring more charge. If this were the case, then "all" that would be necessary to continue to charge a black hole would be to increase the energy of the beam of electrons that are shot at the black hole to overcome the Coulomb repulsion. You would just need bigger and bigger accelerators to keep charging the black hole up to and beyond the extremal limit. When the black hole exceeds the extremal limit it would become a naked singularity.

The concept or possibility of a naked singularity is controversial - it would allow actual "infinite" singularities to be seen directly in our universe - they would not be hidden behind an event horizon the way the singularity of an "ordinary" black hole is hidden. Indeed, a cosmic censorship hypothesis has been devised to prevent naked singularities from occurring. There is good evidence for this hypothesis but I don't believe it has been convincingly proven in all cases.

The real reason why adding charge to a black hole cannot make it become super-extremal is because when you add charge, you are also increasing the electrostatic field energy of the black hole which then has the effect of increasing the mass such that the $\frac{Q}{M}$ ratio continues to stay below the extremal limit of $1.0$. See this question and answer for the calculation of this effect.