MY Ds used to do this at 2 and a half - he dropped his slepp soon after but like you I KNEW if he didnt have a nap then he would be overtired at bedtime and not sleep properly.
There was no way he would go in his cot or nap on the sofa so I got threw it by either putting him in his pram/pushchair and going for a lovely walk - he woudl drop off, I would get some exercise and could have thoughful time as I was walking.
Rainy days I would go out int he car laden with some trashey magazines and as soon as he nodded off I'd pull up, get the mags out and chill
He's now 4 and still gets tired sometimes so we now have 45 mins/1 hour on the sofa reading or watching TV cuddled up - just enough for him to re-charge his batteries