How can you imply that your narrator is unreliable without leaving their point of view?

Before asking how, you should ask yourself why.

Much of the fun of an unreliable narrator is that it subverts expectations. I mean, you could go I think it's the Iain Banks route and have your narrator straight-up say they've been accused of being unreliable. Or you could just write things from the narrator's pov that aren't necessarily true.

I personally love doing the unreliable narrator thing in 3rd person pov. Nobody expects it. Third person is supposed to give facts rather than biased opinion, yet close 3rd person is basically 1st person with the pronouns changed. So I'll state things as fact in the non-dialogue narrative that are actually just mistaken beliefs of the pov character.

Right now I'm working on outlining a story where one of the main characters is a vampire who can erase other people's memories. So there's a key scene that sheds light on his personality that isn't going to crop up until much later in the book than it actually happens, because he erased the memory of it from the other person involved. Plus there are a lot of scenes that are going to be from his pov where I disguise his true motivation, so he seems like a villain right up until the big reveal. But in order for the big reveal to seem like it's answering questions rather than creating new ones, I have to drop hints that not everything is as it seems. Such as the original scene mentioning a moment of disorientation (during which the conversation that got erased from her memory occurred).

Another part of it, in this case, is genre expectations. It's a romance novel, so obviously the “hero” can't be straight-up evil. But on the other hand, maybe he's just misguided and needs the heroine to show him the error of his ways.

Another book I've written with excellent “unreliable” 3rd person narrator scenes is Bite Me. I won't spoil the ending, but there are several scenes from the pov of an FBI agent who goes by the code name of Destroyer. Since I have her think about herself using her code name in the scenes where she's working for the FBI, the reader is left guessing as to which character in the book she actually is.

Another technique I use is for someone to state outright in their thoughts something the reader knows to be untrue, for instance a vampire slayer thinking about how vampires are evil and must be eradicated when the previous book was all about a not-evil vampire who was ready to sacrifice himself to save his soulmate.

In conclusion, while I'm not a huge fan of the unreliable narrator trope in general, from my perspective a lot of the fun of it stems from the fact that the reader doesn't initially know the narrator is unreliable, and only really picks up on it the second time around. To me, that's a key component of great literature: the ability to read a work multiple times and get something new out of it with each reading.