Cute problem
The thing with wood is that its difficult to lubricate. First, you should find the point of squeaking. push down on the mattresses and try to find where the sound comes from. It is possible that there's a metal/composite joint somewhere between the wooden pieces. Then you just take some general lubricant (check your hardware store)...and spray it there.
Squeaking means that 2 different materials, or 1 springy material, are being squeezed. Is it possible that your mattresses are squeaky? Mattress springs often make squeaky noises. Try a different mattress.
Lastly, remove your mattresses. Check all wooden joints...make sure all the screws and bolts are tightened well. A loose wood plank can cause the squeaking too.
Hope that somewhat helps.