With my kids... I had a routine... for naps. They also were NOT "portable" nappers... they would ONLY nap if HOME... and in their crib. I scheduled myself, around their naps.
If they did not nap... they were fussy OVER-tired Trolls.
At 2 years old, sleep/nap tweaks happens. BUT your child is still displaying tiredness.... so he needs to nap.
What time are you making him nap? Or does it vary every day???
The best thing is, is to have a routine about it... not just 'wait' for him to look tired. Because by then... they are already OVER-tired of you have missed the window.
Over-tired kids, also fall asleep worse, cannot sleep well and wake more.
You need to try and be more consistent... in his nap times.
One important thing is... do NOT have lots of activity, right before naps. Otherwise the child CANNOT "wind-down" and key down... and it sabotages their falling asleep ability.
BEFORE nap time, at least 1 hour PRIOR.... be HOME.
Have a routine of winding-down.... make everything turned off and quite and boring. Verbally cue him.... "we will get ready for nap..." and then do so. With QUIET things. Not active activities. MELLOW things.
If he is tired, don't bother feeding him and doing all those 'chores' beforehand... just let him nap and get him off in the routine. He can eat later.
OR... you NEED to have lunch time... earlier. You need to 'anticipate' the process.... and so it is not all 'rushed' and then you miss the window.
Make your timing of everything... earlier.
For example: you said this morning he was tired (already) on your way home "for lunch.... but you had to feed him and diaper him before napping...." Well, that whole process can literally take 1 hour MORE at least..... by the time you got him ready for nap. By then it was TOO late. You missed the window.
So... heed to that. Don't come home... late... and then have to feed him lunch. FACTOR IN, into your errands... what time you NEED to come home BY... so that you DO have enough time to come home, feed him/diaper him and WIND-down... not it being too late.
For me, I know when I put my son to nap. He is 4. SO... when we are out doing errands/activities or whatever... I ALWAYS come home.... BY the time he needs to nap... AND I factor in our home routine... ie: lunch, winding-down and how long that will take, etc. SO... we come home WAY before that time... otherwise, everything and his naps... just gets too late and just too late.
No matter what... my son naps at a certain time. He knows that, I know that. If my son does not nap... he is a MONSTER Troll. And it ruins the whole rest of the day. Him being over-tired.
You need to have a more regular routine about it and timing of it. It is all about timing.
Nap when he naps.
OR... lie down too... and with him.
all the best,
Susan