The best chance to have long lasting colonial empires would be no American Revolution and The British Empire gradually evolving into an Anglo-American partnership, without the ARW the Spanish Emprire will gradually reform to give control of the colonies to the local withes under the sovereinity of the Spanish monarch , maybe with the center of the Empire eventually moving to Mexico City.
Having the american manpower, the Brit Empire instead of becoming overstretched, like OTL, will have the manpower to swallow China and reduce Japan to a satellite state, Africa will be divided among European States like OTL, the Ottoman Empire could also be divided/vassalized by several European Powers, after this, there isn`t any non-European state remaining independent beyond Japan, and no case of a sucessful colonial rebellion to provide an inspiration, as the Anglo American Empire will be the hyperpower around the 1890's there also will not be World Wars to disturb the status quo, so the World could stabilize in a very long lasting Belle Epoque