How to measure amount of oxygen (or carbon dioxide) in air?
This is untested, but I think it might work. You could light some fuel on fire inside the closed container and see how much of it burns (just put the cup of fuel on a kitchen scale) before it dies out and than back calculate how much oxygen was present. Preferably you should take a fuel that burns easily to make sure that the total combustion reaction is the only reaction that occurs. Also if you want to repeat the experiment every hour or so, you want to be sure that the fuel does not evaporate (substantially) because that might cause the entire container to light up when you try to burn the fuel.

I am not really sure which 'household' fuel would be a good option, but maybe one of the other people on this site have suggestions?!

You can probably use one of those candle lighters and stick the long side through a small hole in your container and than seal the rest of the hole to be able to light a fire inside, without having air flowing in or out.

Just be careful not to set the plant (or anything other than the fuel) on fire!