Is prayer acceptable when wearing trousers that have a wet spot the size of a coin, which the worshipper is not certain is urine, knowing that he suffers from urine drops after performing istinja'?

The wetness that affects the garment must have originated from the two private parts or be an impurity from other sources, such as blood or pus. If it is sweat or wetness from water, or if you are unsure about it, then its ruling is purity. The fundamental principle for things is purity, and a ruling of impurity is only made when there is certain proof.