No, but on the signs
They did spend $250,000, but that included making and installing new signs for the airports.
The original article at earthtimes.org (archived) claims:
GLASGOW, Scotland, Nov. 28 Scotland has replaced its airport signs proclaiming the country to be "the best small country in the world" with a new slogan: "Welcome to Scotland." The new slogan, which was revealed Tuesday after six months of development and $250,000 spent on the project, is also printed on the posters in Gaelic as "Failte gu Alba," The Times of London reported Wednesday.
Confusingly it is tagged with US World News even though earthtimes.org is a British website.
According to articles from BBC, the Scottish Daily Record, and The Times from 2007, they spent £125,000 on the change. Thanks to a strong pound or a weak dollar, this was worth 258,900 USD in November 2007.
Note that this only covers the signs at the airports:
A government spokesman said the £125,000 cost of the displays covered the new artwork, printing and installation.
The same article also defends the cost as simply part of the normal budget, included in the long term planning:
The cash came from existing budgets as the Best Small Country campaign was due to come to an end.