During which phase of the cell cycle does the organelle replication take place?

Actually, organelle replication, occurs during the G2 stage of the cell cycle. During this stage, organelles are replicated and proteins are synthesized. The G2 phase follows DNA replication which occurs during the S-phase. The actual cell cycle begins with the resting phase called G0, followed by the G1 phase, the S and G2 phases which are known as interphase. The M or mitosis phase is when the cell divides into two daughter cells. During G0, cells are at "rest" and during interphase--G1, cells grow and synthesize the 20 amino acids needed to manufacture proteins later on. During S phase, DNA synthesis occurs. During G2, production of microtubules occurs and other organelles are manufactured. During M phase, mitosis occurs and when the two daughter cells are produced, they enter the G0 step once again.