Edit: Wow I wrote more than I thought. Probably could've started a couple topics myself here
tldr - most avns are hard to get invested emotionally in (porn logic moments etc), so I almost never cry.
Clover and Over by Eevee, is the only one that got me.
I know I've been glassy-eyed playing a few avns before, someone here mentioned Ashley from harem hotel as an example. To make me go from being irritated/annoyed with a character to caring about them, that probably needed some tearing up going on.
I'm pretty sure the only avn that made me cry was a short demo/prologue? called
Clover and Over by Eevee and Floraverse, it's on Itch. Also a Queer/Furry game if that's not for you, but the protagonist had some very real concerns about a sexual encounter they had and were anxiously obsessing over it. It really resonated with my real anxiety and fears about sexual intimacy with real people.
Oh, I think Luna's story in Eternum had me teary, but most avns struggle in the "novel" part of "adult visual novels". If the protagonist is supposed to be an player insert, I'm often too busy making my own headcannon of how I'd handle a situation better, for instance: Harem games are often the closest thing to polyamourous games, which is somthing I desire in avns, but they are rarely ever good enough to be a believable narrative (so many just have the girls all magically be so invested in Mr. Average that they sacrifce their feelings about other women just to have their chance with him) also Harem=/=Polyamory as far as people are concerned genre-wise so I kinda need to make my own headcannon playing those. All that said, makes it pretty hard to get super invested emotionally when you're mentally rewriting or ignoring the story to fit your preferences better.