As far as I can see, there are only the following logical alternatives;
1.
Revoke Article 50 and remain in the EU. Obviously, some people would like this. However, it goes against the result of the Referendum, and is considered politically impossible.
2.
Border between Northern Ireland (NI) and Republic of Ireland (RoI).
Theoretically, this is possible, because they already have different legal systems, different health service, different education, and especially a different monetary system.
However, this would break the terms of the Good Friday Agreement (GFA), which forbids a border.
This may provoke violence from the IRA. (I have NOT read the GFA, but going on media reports.)
3.
Keen Brexiteers have stated goods can be checked away from the border electronically and claim this is done elsewhere. The EU state is can’t be done.
4.
Under the terms of Theresa May’s Withdrawal Agreement (WA), The UK would stay in the single market and customs union, until all other 27 countries agree, thus avoiding a need for a border. But we would have no MEPs, and no EU commissioners. Brexiteers complain this would make the UK a colony of the EU, accepting their trade rules, etc without any say in anything.
(This was presented and voted against in Parliament 3 times)
Note, there may be other things purists dislike about the WA, but this post is on the Irish ‘Backstop’.
5.
The border can be in the Irish Sea, between the Rest of the UK (rUK), and the whole of Ireland.
Theoretically this could be done, as there are already Border Inspection Points at Belfast (BIPs), which could be extended. This currently allows for a certain percentage of livestock to be checked at the ports. Neither the DUP, nor MPs, would agree to this, as over time, Northern Ireland would become more aligned with the EU, than with the UK, and would in effect herald the breakup of the UK.
It has been suggested that this would provoke violence from the unionists.
6.
The Border could be in the English Channel. This was sort of suggested in one paper last week, maybe jokingly, although I have heard personally of someone mention this.
The theory being that if most of the RoI and NI trade is with the rUK, then this would make sense. However, neither the EU, not RoI would ever take this suggestion seriously.