There's no need to refrigerate coconut oil. It'll last a long time—up to two years—in your pantry. Just keep the lid on tight. Depending on how warm it gets where you live, your oil might go from solid to liquid in the jar.
Coconut oil has a relatively low melting point—about 76°F, so it will almost definitely turn to liquid on your shelf in the summertime. And though you might be tempted to store your coconut oil in the fridge, that actually makes it harder to use because the coconut oil turns into a solid paste when refrigerated.