I’ve got a punctuation Jones

If it is meant to mean "The Jones Family", then the appropriate rendering would be THE JONESES, as in the old phrase KEEPING UP WITH THE JONESES.

Neither JONES'S nor JONES' has grammatical precedent, to my knowledge. The former would (formally) mean "belonging to [a single person called] Jones", and the latter would mean "belonging to a group of people, each of which is called Jone"!

THE JONESES would be the correct plural of JONES.

(The only other possibility, but one which I think looks a little clumsier, stylistically, is THE JONESES', with an apostrophe after the final ess, which would be shorthand for "the place belonging to the Jones family".)

Speaking practically, the best thing you can do is what the customer insists upon. But have one of your co-workers in the room with you when you capitulate, so that the customer cannot come back later on and blame you for the error.

The point you ended up arguing on was not really how to make a plural of the surname Jones, but rather how to make the possessive form - and for that, either Jones' or Jones's is correct (e.g., the Jones' car; the Jones's car: the car that belongs to the Jones family). But not, as Dave points out correctly, what you want here. 'The Joneses' is correct.

Incidentally, I think the possessive form (Jones' or Jones's) will be pronounced the same way when people read it out, irrespective of how you write it - i.e., people ignore how you write it. :-)

As the customer is paying for you to make this sign, I suggest that you use the form that the customer wants.

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It depends on whether the point is that the trailer is where the Joneses can be *found* or whether it's that the trailer *belongs* to the Joneses. In the former case, it's "The Joneses [live here]", in the latter, it's "[this is] The Joneses' [place]". I can't really see a reason to suppose it's one over the other, besides which the customers asked for.

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Jones's is never correct in any circumstance.

Try using a non Jones example and apply it to the Jones e.g.

Try a family with the surname Mills. The item would be the Mills' car. You can easily insert or delete the Mills' (family) car. It would never be the Mills's ever!

Chuck,
you're right (except that you spelled "Joneses" wrong). It should just be "The Joneses", which is simply plural for Jones. Just like in Avram's post: it's where the Jones family can be *found*. If they want to specify that the trailer belongs to them, it should be written The Joneses'.

Of course this mistake is so common that it's probably "standard" usage in some parts and you would look out of place if you didn't use The Jones's. However, that seems to imply only one Jones, imo, and not an entire family of Joneses.

Brigid, the Chicago Manual of Style offers "the Williamses' new house", so obviously this is a matter of style. Jimmy Mills's car or the Millses' car would be then seen as correct usage.

As long as there's a "the" in front of Mills, however, it's obvious that we're talking about a group of people, therefore "the Mills' (family) car" can't really be misunderstood either.

The Oxford Companion to the English Language page 75:

the apostrophe of plurality continues in at least five areas:
[...]
(4) In family names, especially if they end in -s, as in keeping up with the Jones's, as opposed to the Joneses, a form that is also common.