Hi there, these would be my ideas ... maybe some help?
- Try a good studd finder, they may go through two layers of boards to see the joists.
- If you have spare boards then you could drill a tiny hole to start with (about where you would like the centre) then if that doesn't hit a joist open it up a bit so you can get a jigsaw in there. Then start to cut outward in each direction until the hole is large enough or you come to joists.
- Interms of cutting it once you have determined wher the joists are ... you could mark the outline of the hole then use a circular saw (i'd set the depth shallow just in case you missed a joist) then you could go around the edge with a router to clean it up ... you could even rebate it to make a nice draft proof seal on the new trapdoor.
- If possible chose a location that is out of the way ... like in a wardrobe, under a bed or a rug?