Romance, love, sex, heartbreak - these are often as key to Buffy as the monster violence and snarky asides.
I've seen from personal experience that a romantic plot (especially a complicated one with multiple interested parties where someone's bound to get hurt) can turn a regular monster-hunting game into full-on Buffy with all the trimmings.
There are articles, even entire sourcebooks and indie games dedicated to romance in gaming. They show how it can drive plots like nothing else, and also generally demonstrate that the players have to be willing to let their characters get hurt emotionally for it to work.
Romance can be an awkward thing for a lot of gamers, so there are some who won't want to go for this. If that's the case, there's no point pushing and annoying your players. You could suggest a limited single-episode romance plot and see if they're willing to try it in a clearly separated box, but the answer might still be a no.
If Young Player Characters In Love is a no-go consider a romantic plot at one remove, with NPCs as the fools for love. It'll lack the defining hugeness of a PC-centric affair, especially if you don't like playing multiple NPCs in a single scene, but it's enough to reflect the importance of love in the setting hopefully without squicking anybody at the table.
Anyway, PC or NPC, what does a love-centric Buffy story involve?
Generally, a happy couple is a subplot, not a plot. We're here for angst, people.
So Character A loves Character B. Does Character B reciprocate? What if they're dating Character C - who is a friend of Character A and an ally in the fight against evil? And Character D is into Character A too.
And Character C's parents don't approve of Character B, and can good friend Character A cover for them?
And Monster X has the hots for Character B as well. Much to the annoyance of Monster Y, who has loved Monster X for centuries and so wants to kill Character B, even though that screws up the plan to use Character B's power to open the portal to Dimension Z...
The Smallville RPG (a game built around the dramatic interconnections of a show that could at times look a lot like a Superman fan's Buffy game) has everybody's power defined by their feelings for everyone else, complete with antagonist PCs. Its relationship maps might be a good guide for when the love dodecahedrons in a game get hard to follow.
And that's just regular could-happen-in-any-high-school-drama love. Add love spells and succubi and things can get way more puzzling. The Sexy Monster is a recurring subset, sometimes MOTWs who just look the part and sometimes Big Bads or Big Morally Uncertains or Big Damn Heroes or some shifting combination of all of the above. After all, we're dealing with vampires here, and while regular Buffyverse vampires are mostly just snarly and bumpy, there are plenty who still have the allure of eternal youth and a liking for love bites...
Hope has a new guy, which among other things reminds her former guy in the band how cute she is - nothing like being off the market to make you tempting. But is it just jealousy that makes her ex suspect the new guy is connected to the girl found on campus with her heart torn out?