Private burial plots, so called “home plots” began to be seen in Iceland in the late 1800s and new ones were being added until the 1960s, when a stop was put to the practice by law. However, it is still allowed to bury people in them if there is room. There was one on a farm near where I grew up, looking pretty similar to the example below.
There are about 160 of them in various parts of the country, including a grand one you can see in Borgarfjörður right by the Ring Road (Route 1). I’ll try to remember to snap a photo next time I’m passing that way and post it some time.
This typical example is located near the old Kolviðarhóll farm right by the Hellisheiðarvirkjun geothermal plant.