Pertinent questions are: do you want the changes to be a total surprise, and do you want the area to be relatively small (such as between two towns 20 miles apart)?
In either case, you're in trouble. There are means both to add and subtract altitude, but they both involve a lot of generalized energy which is hard to miss if applied over a short time.
Mountains can be created in two ways: volcanic eruption and thrust faulting. Volcanic eruptions can provide fairly rapid mountain building, but this is accompanied by earthquakes and major emissions of ash and/or nasty fumes. Thrust faulting (such as created the Rocky mountains) produces even worse earthquakes than volcanos do.
At the other end, floods can make major changes in landscapes, the most massive event known in the US being the creation of the Channeled Scablands. This produces quite distinctive landscape features, and the limited existence of such features is very strong evidence that the Biblical Deluge did not happen. But again, you're talking about really massive incidents, and such things would be noticed locally.
More in line with what I think you're after, rivers do change course spontaneously, and this can occur without too much fuss. Oxbows can short-circuit in a matter of days, producing new islands. At fairly large intervals (say, a thousand years) you can get a really major change in river course as a river "falls off" its delta. As a matter of fact, the Mississippi river is overdue, and only massive efforts by the Corps of Engineers have prevented the Atchafalaya River from leaving New Orleans cut off from the river.