My understanding of the law is that Irish and British citizens are allowed to beg in Ireland, but that EU citizens (excluding Romania and Bulgaria) must be able to support themselves (through savings or work) to be permitted to remain in Ireland, and Romanians and Bulgarians must have a work permit to remain here longer than 3 months.
It seems to me that there are suddenly large numbers of non-Irish or British beggers in Dublin (and probably in every city in Ireland). One advantage of being outside Schengen, we are always told, is control over our borders. So if these people are breaching the terms of their residency, why are they not deported?
We don't have ID cards in Ireland, so it might be difficult for the Gardai to determine who is permitted to beg and who is not. So how about we issue a begging permit to the Irish and UK citizens who are homeless or which to beg. Anyone without the permit would be arrested and, if their immigration status allows, deported.
I imagine the Irish and UK homeless would strongly support such a scheme.