Certainly the Ring's actions can be taken to imply it has a conscious will, but I'm not sure there is one action it performs that can be said to prove that. What exactly was its 'program'? Changing its size doesn't prove it was conscious in any way, only that it could change size. Of course, 'absence of evidence isn't evidence of abscence' & the fact that one cannot find unequivical proof of its consciousness doesn't actually prove it isn't conscious. On the other hand there's Occam's Razor: there's no necessity for the Ring to be conscious - ie we don't
require that hypothesis.
Were the Silent Watchers conscious - & if so, how, to what extent & in what way? Was Turin's sword (or the Troll's purse if you want to include the Hobbit)? If any or all of them
were conscious it would require an explanation of how a living mind could be bound into a 'dead' object & I think we're venturing into zombie territory there.
Of course, it could be that such a form of 'life' did exist in Middle earth...