We don't have 'The' rival - an frankly I don't think we ever will...unless somehow, someway we battle Utah for supremacy in the Pac12 for a decade or so.
To have a 'Rival' I think the biggest factor becomes, are the two rivals recognized by outsiders as being equal to one another competitively over time, and more logically tied to one another than any other opponents. Michigan v. Ohio State and Alabama v. Auburn come to mind. They are pairs that are on the same level of competition, are close enough that their fans will live near, work with, and inevitably interact with regularly.
So for us we can have conference rivals - (I personally see UCLA and Cal as the most fitting) but acknowledge that any schools other than Utah will always have more bitter rivals than CU when they are asked.
We can have historical rivals - NubU and NotreDumb
...and while I hate to admit it, we will always have the sheep....
Until they have fallen so far that we can walk into a Garts, or a Kohls, or even a Target and not see one stupid green and pee t-shirt we must beat them down as we should any aspiring rival. I do believe there is something to be said for being bigger than the rivalry they try to push on us. It requires making the contests in which we compete such perennial wood shed affairs that they get tired of playing, and it requires not stooping to their level when we have to attend their administration of humility in Denver. Go to the game, tailgate with fellow Buffs, don't engage, don't fight - just watch it as if it was UTEP or some other non-conference cream puff (not that any non-conference opponent can be considered a cream puff yet). As for the team - they will need to have this one on the radar as long as the series continues - CSU will always be gunning for the Buffs.
I do hope that in 10-15 years we have become 'hated' in the south - with key victories against the remaining 4 programs to crush whatever aspiration they each had before playing us, and of course by that time we had better be 'in-the-mix' year over year for conference championships. USC and UCLA are going to be targeted, but to consider them rivalries before we have done anything to set them back seems premature. Hopefully by that point Utah will have become our new CSU and CSU will have become our new UNC. UNC in turn will have risen having been once led by Tad - and will be a fitting and competitive 'Rival' for the lambies.