Um. Let's see. To do it during BtVS season three, they'd have had to completely change Wes's initial personality profile and his interactions with Buffy *and* overcome the whole Watcher/Slayer teacher/pupil hurdle, which was pretty entrenched if implicit. No dice. It might have happened in season four if Wes had decided to stick around and tough it out and if Buffy had been more mature and forgiving toward him over their differences.
So let's see....
He'd need a good reason to stay in Sunnydale after being fired. He'd either have to play the supplicant to Buffy, asking her to accept him in some supportive role, or he'd end up in a motel room a la Faith, drinking and brooding on his failure and getting started along his Dark Wes streak several years early. I like the second option. You could play with that--in fact, it's kind of interesting, because as peasant_ has said, and as I've said as well, Wes's forced growth from milksop to ronin can be a bit hard to swallow, as it's occurred in canon. So why not swallow it more quickly? Seriously--I think the transformation would actually have worked better if it had been faster. Because then Wes's brief, buffed-and-polished tenure as watcher elect would have been much more apparent as a facade. We'd have understood, if we'd seen his soufflé of ego collapse along with the high school, that he'd been desperately trying to fill his father's shoes and uphold centuries of tradition, and that there'd been a Wes inside Wesley all that time, just waiting to come out.
So, Through-a-Shot-Glass-Darkly Wes has stayed on in Sunnydale, and he's living out of his suitcase, council funds cut off, and he's drinking and he's stubbled. And he still believes he was right, and Buffy wrong, but feels guilty nonetheless. He's spent the summer isolated and berating himself for perceived faults--including cowardice--having been tongue lashed by his father into a deep funk. So he's been playing rogue demon hunter as penance for his failure, trying to build up experience, field knowledge. And as S4 opens, Buffy and gang run into him in a graveyard; they're surprised, because he's managed to avoid them all summer, and he tries to blow them off now, but Buffy won't let him. He's grim and dark and proud and not especially willing to bend toward her at first, but she feels bad as she's faced with the consequences of her actions, and realizes the effect they've had on his career and circumstances. (Buffy's not truly mean-spirited or hard-hearted about fellow white-hats.) So she makes some concessions and he in turn folds with relief and lets himself be drawn back into the fold; and of course all we need to do is imagine the S4 BtVS meeting between Buffy and Wes playing out as S1 A:tS played out between Angel and Wes.
Give Giles a different apartment or a reason to move and you could imagine him inviting Wes to take the spare room. Give the two of them some kind of project so they're not kicking around uselessly--like maybe the council comes around toward supporting them again because they're being made uneasy by the appearance of the Initiative commandos. Or simply because Travers, et al, can't accept loosening their reins on Sunnydale or the slayer. (Which actually makes much more sense than how they did.) Cut out the Parker arc and launch into Riley earlier; make him more of a bad boyfriend. Draw parallels between Wes and Riley over the first part of the season: make Professor Walsh a man, make him Riley's dad. Give Riley huge, honkin' daddy issues; he's following in dad's bootsteps, trying to live up to his mission. He looks like the perfect boyfriend to Buffy at first, because he represents strong family values; he's tight with his father, and Buffy is wistful and touched by their closeness. You can just imagine how she'd compare her circumstances to Riley's and wish that her own dad could know what she did, and be proud of her. (And I seem to have moved into drawing parallels between Buffy and Riley now instead of Wes and Riley, but hey, that can work too.)
But as Riley and Buffy grow closer, Wes is concerned. He sees a darker side to Riley, a ruthlessness and fanaticism below the clean-cut soldier-boy surface. When Riley starts to work with the Scooby gang, he and Wes start to clash; Riley doesn't take either of the ex-watchers very seriously. He mocks their Britishness (though he's careful not to offend Buffy too much on their behalf), and their cautious approach to research strikes him as effete. During this time, Wes starts to show more obvious signs of interest in Buffy; Buffy is oblivious, but Giles notices. (In fact, if you wanted to remove the Wes/Cordy stuff from S3, Wes might have already been showing foreshadowing signs of interest in Buffy then.) He tells Wes to get over it, says that it's bordering on inappropriate even though Wes is no longer her watcher; but he's also understanding.
We'd have to see a lot of new facets to Wes during this stretch, as he overcomes the first impression he made during S3 and shows that in fact, under his starched exterior, he always had knowledge and skills--they just hadn't been fully exercised.
So things come to a head near the end of S4 and Buffy realizes that Riley has been playing her in some way, using her--major, major betrayal and angst as her first non-Angel relationship proves itself hollow. Like, imagine if Joss had come up with the idea of flatlining slayers before fan-fiction writers had; say Riley Senior & Son kidnap Buffy and intend to kill and revive her endlessly to build an army of slayers all their own. Because darn it, what's up with slayers being in British control anyway? This world and this fight should be run properly and professionally, by the U.S. of A.
Wes and the Scooby gang rescue Buffy; Wes in particular showing heroism and helping get her safely out of the Initiative when she's badly hurt, or something like that. And a battle between the forces of the council and the Initiative are waged and as we close off the season, we end on a romantic, upbeat note as Buffy finally starts to look at Wes in that way, with respect and appreciation and longing.
S5 would open with them still feeling their way into the relationship--they never took that next step over the summer because Buffy had been so hurt by Riley she couldn't leap into another romance. There'd need to be some external crisis to bring things to a head, to make Wes go for it, to make Buffy succumb. Or vice versa. But a nice crisis occurs and they smooch and yowza, fireworks! they're tumbling to the floor of a crypt! they're ripping off each other's clothes!
And they live happily ever after until Wes is killed in a tragic smelting accident. Or, you know, smashed to bits by Glory at the end of S5. Sniff.