The timetable has a major effect. If you have thousands of years, you give everyone really good health care, a good standard of living and perfect contraception, then subtly use your reproductive technology not to completely sterilize the population, but to reduce growth to the point where the population declines over many generations. All the while, I'd be building habitats for my alien race underground, underwater and in places that are incapable of supporting human live (South Pole, Sahara Desert, et cetera). Once the population drops below a certain level, you build them in Truman Show-style habitats and maintain the population for entertainment purposes.
Or, if you really don't care about genetic purity, just genetically alter your race to be really sexy humanoids that can interbreed with humans, and then screw until everyone's an alien-human hybrid.
Or create really cool virtual reality worlds, where people can have their bodies stored in suspended animation for centuries while their minds are uploaded into these simulated worlds where they can do anything they want, and tell them you'll take care of the world while they're frozen. You don't even have to lie to them. They go live in the perfect fantasy world while you run the planet, and just keep a few habitats for the ones who decide to come out of VR or don't want to go in in the first place. For the people who absolutely want their own planet and had the idea of things not being "real", find a nice planet to terraform and give them everything they need to do it. They build a civilization, forget their zealot origins, and then you just start the process over on the new planet.
Or, giant solar shade that causes the entire planet to freeze. Remove the shade after a few thousand years, once all the humans have exhausted their fuel supplies to keep warm. Live in the perfectly preserved homes of the dead humans and dine on their thawed flesh.
