The bone marrow is the primary site for the production of red blood cells after birth. This spongy tissue found in the cavities of bones is rich in stem cells that differentiate into various types of blood cells, including erythrocytes, or red blood cells. The process of producing red blood cells is called erythropoiesis, and it primarily takes place in the red bone marrow.
While the liver and kidneys play vital roles in the body, particularly concerning metabolism and regulating blood pressure and fluid balance, they do not actively produce red blood cells after birth. The liver is involved in blood cell production during fetal development and also helps manage iron metabolism necessary for red blood cell formation, but its primary functions shift after birth. The kidneys play a regulatory role through the production of erythropoietin, which stimulates the bone marrow to produce red blood cells, but they do not produce these cells themselves.
Thus, bone marrow is the correct answer due to its crucial role as the primary organ responsible for the continuous production of red blood cells throughout adulthood.