Actually, the UK government has a very good solution to the Irish border issue, which the Irish are in favour of. It is the EU that will not allow it.
UK politicians before referendum pointed out that they were willing to preserve the CTA (common travel area between Ireland and UK) which predated -- but importantly doesn't supercede the EU. Irish politicians pointed this out but were largely ignored by UK press.
>It is the EU that will not allow it.
I suspect you're alluding that this is somehow the EU's fault. It really isn't -- and the finger points 100% at the UK. There are treaties and agreements going back decades including for instance the Good Friday Agreement on which all peace in N.Ireland is largely credited. The lack of a border is mandated by this international and binding agreement which UK seems happy to simply ignore.