Definitely don't use that translation. It's pure junk.
This would be my attempt at a translation: "Cosc ar Ghaeil, ar dhaoine gorma agus ar mhadraí. (literally: prohibition on Irish people, on blue people (in Irish, black people were traditionally referred to as blue people) and on dogs."
Some provisos:
I'm not sure if you should use "Éireannaigh" instead of "Gaeil". They both essentially mean "Irish people" but I'm not sure if the word "Gaeil" also implicitly includes the Scots (especially Highland Scots) and Manx, i.e. like the English word "Gaels", in which case maybe "Éireannaigh" would be better.
Instead of "ar dhaoine gormacha", maybe "ar ghormaigh" would work i.e. turning an adjective into a noun. This works in English but I suspect it is also acceptable in Irish.
Repetition of preposition: In English, instead of repeating a preposition in the context of a word list, it often suffices to say it only the first time e.g. "Prohibition on Irish people, blue people and dogs", instead of "Prohibition on Irish people, on blue people and on dogs". I'm not sure if this would be acceptable in Irish, but if it was, the question then arises as to whether or not the lenition associated with the omitted instances of the preposition should also be omitted. There is some limited discussion of this topic at the following:
viewtopic.php?f=28&t=2321&p=21140&hilit=preposition+repeated#p21140. But in the case under discussion here, I somehow think it would be better to include all three instances of the preposition.
As Djwebb points out though, the existance of such signs seems to be more of an urban legend than anything else.