You can of course, drink coconut oil for constipation. But when you drink, make sure your stomach is not empty. It's counterintuitive to swallow coconut oil down on an empty stomach. This is because coconut oil will quickly digest and break down to stimulate bowel movement.
And if you drink like 2 tablespoons or more, you may suffer a diarrhea effect that can last the entire day. Which will make you run to and fro the bathroom. Taxing, especially for seniors.
Having said that, I'd suggest that you snack first before drinking coconut oil for constipation. Or simply add coconut oil to a light meal. This will lessen the diarrhea effect from consuming coconut oil.