Check time since last request
If this is the easiest solution for you to implement, go right ahead. Worst case scenario, it's too slow to be practical and you'll need to find a better way. Any other scenario, it's good enough and you can forget about it.
Honestly, it'll almost certainly be efficient enough to serve your purposes. The number of users at any one time will very rarely exceed one. An SQL query to determine if the timestamp is over a day before the current time will be quick, enough so that even the most determined gas-hole(!) wouldn't be able to cause any damage by spam-clicking the button. I would be very surprised if you ran into any problems.
I've a bit of code that involves sending an e-mail out to my housemates when it's time to top up the gas meter. This is done by pressing a button and picking whoever's next from the database and sending an email. This is open to a lot of abuse as you can just press the button 40 times and send 40 emails.
My plan was to add the time the e-mail was sent to my postgres database and any time the button is pressed after, it checks to see if the last time the button was pressed was greater than a day. 
Is this the most efficient way to do this?
(I realise an obvious answer would be to password protect the site so no outside users can access it and mess with the gas rota but unfortunately one of my housemates the type of gas-hole who'd do that)