I'm going to be a bit more ambitious than others here. To maintain the 18th century status quo, you need to change a host of social factors that started to upset things into the long 19th century.
My list of "things you need":
1. Abort Romanticism before it is born
2. Avoid popular-nationalist revolutions
3. Maintain a stable(-ish) balance of power such that the great powers of Europe don't get desperate enough to try levee en masse.
4. Keep the Enlightenment intellectual climate active and engaging
You have to get there from someplace though, as this quartet won't emerge fully formed from the head of Zeus.
My suggestion is to delete or at least greatly modify the Seven Years War. That conflict strained the finances of France and Great Britain, and was thus a contributing factor toward both the French and American revolutions. Further, Fredrick the Great's campaigns gravely disrupted the Central European status-quo, weakening the position of Poland and Austria. As the latter was a multi-national Empire with no use for base nationalism, keeping it strong (or at least stronger) reinforces traditionalism in Germany, Italy, and the Balkans. Keeping Russia less involved in European powerplays for a bit longer is another bonus.
Deleting the Seven Years war hardly means that Europe will live in peace and harmony until the End of Days, but if European Wars maintain a lower intensity and less global character, there is a far lesser likelihood of military-social change on the order of OTL.
Without the American and French Revolutionary Wars, and lacking the Napoleonic Catastrophe, the 'Long 18th Century' will chug along quite a bit longer more or less intact. I don't imagine that you can freeze the European cultural environment forever though, as at the very least technological change will start to undermine traditional social structure before 1900.
Further, keeping the American colonies tied to Great Britain eventually means that they must come to a political accommodation. While this in of itself does not have to be contrary to the Age of Enlightenment or otherwise disruptive, the growth of the American colonies yoked together with British economic development will begin to irrevocably alter the European balance of power; particularly as industrialization sets in.
If London still maintains itself as the swing vote in European power politics, then this might be all to the good for our objective here. Provided that British colonial nibbling and economic expansion doesn't break European politics, Britain may well serve as the enforcer of Europe's status-quo; and if the British model of a small professional army appears successful enough in whatever coalition warfare erupts, another leg of 18th century traditionalism gets reinforced.
Alas that we may have to sacrifice Fredrick the Great (or at least his campaigns) to achieve this challenge, but I suspect it may be the best and most decisive intervention.