D.K.
Put him down BEFORE the signs of being tired start. Have a more rigid schedule. Put him down the same time every day.
At nine months he probably could use a nap in the morning and another after noon. Three naps might be a little much. Mine didn't go down to one nap until after 12 mos.
Being overly tired will backfire and wire them out, as I am sure you have figured out.
I would have him get up, eat, change him, play for a bit, hugs and cuddles, nursing then lay him back down about two hours after he gets up, then leave him there, for an hour even.
Then later in the afternoon around 1 or 2 pm lay him back down. Don't wait for cues from him, he needs a schedule, he will get it after a while. If he lays there and plays so be it as you cannot force him to sleep. Giving his body cues and a schedule will save your sanity too.
I have very rigid schedules with both of mine, same time every day unless something huge happened to disrupt it, they are still both great sleepers and were great nappers as babies.
Make sure too he has a full belly, is he eating solids on top of nursing? At 9 months his appetite has kicked up a ton and needs more then nursing. Breast milk does not stay on their system long.