Yes, of course. You can store coconut oil literally anywhere. But depending on the types of coconut oil you buy, if it's liquid coconut oil (a type of refined, fractionated coconut oil), then storing it in fridge does not cause much inconvenience since it will always stay in liquid form even at water freezing point (32 °F or 0 °C).
But if it's other types of refined coconut oil (like RBD coconut oil) or virgin coconut oil, then you may have problems using it when you take it out of fridge since these coconut oils will turn rock-solid at temperatures below 76 °F (24 °C). You'll need to warm it up before it turns liquid again for you to use. Otherwise, you'll have a hard time scooping it up for use.
Actually, it's not necessary to store coconut oil in a refrigerator since it contains predominantly saturated fats, which are highly resistant to oxidation upon exposure to heat, light or air, unlike olive oil and others which hold primarily unsaturated fats.
In other words, if you need to frequently cook or bake with coconut oil, or eat it out of the jar, or use coconut oil for your everyday skin care or whatsoever, then keeping it out of fridge even in summer does not hurt at all. You can even store it near the stove so that you can reach out to it conveniently during cooking.
It'll only start to turn bad when it smokes at 350 °F (177 °C). Therefore, you can store coconut oil anywhere so long as the temperature around it is well below that level.
Oh, I have to warn you about thawing coconut oil in case you prefer to store it in fridge. Never open the lid for thawing thinking that this can help coconut oil to warm faster. The surrounding (warmer) air will condense quickly into tiny water droplets and stick on the inner wall of the coconut oil jar. When it touches water, the natural aroma in especially virgin coconut oil may taper off, depending on the quantity of water it touches. Hence, keep the lid closed when thawing.
Of course, there is already some amount of air in the jar where coconut oil is kept, so when you store it in fridge and thaw it even with the lid tightly closed, this little amount of water may contact with the oil and reduce its phytonutrients that give coconut oil its natural aroma. Which is why I never store my virgin coconut oil or refined coconut oil in the refrigerator.