The only solution that seems to meet all requirements is for Northern Ireland to become a largely self-governing province of both the United Kingdom and the Republic. As part of this arrangement, citizens of Northern Ireland would have full rights of citizenship in both countries. To a large extent they already have such rights, but they should be entitled to elect representatives to the Irish Parliament.
Where there was a difference between Irish and British laws, notably in the field of family law, a reconstituted Northern Ireland Assembly would decide which law would apply to the province. Education, health and welfare would all be handled within the province. Ultimately these services would be financed out of local taxation, but continuing subventions from Great Britain would be necessary for some years.
Security would also be handled within the province, but even after the settlement had been agreed, it would take years to build up security forces composed of and accepted by members of both communities. During this time the police would need to be able to draw on staff, including very senior officers, from countries other than the UK or the Republic - from the EU, Scandinavia or the Commonwealth.
This settlement gives the Irish tradition in Northern Ireland parity with the British, which, together with the withdrawal of the British Army, should make it acceptable to Nationalists. But, unlike joint authority, it gives Dublin no executive power within the province. Unionists would have lost nothing except the protection of the British Army, a protection which, given the settlement, they would no longer need.
Unionists would need to be reassured that this settlement was final, and not a step towards absorption in the Republic. Among other guarantees, the Republic would have to replace Articles 2 and 3 of its constitution by articles recognising this settlement.