Yes, in fact there are some Tony/Jarvis fics. Sadly, not nearly enough.
I included some threesome and gen fics in this list.
Cool Blue Reason
Summary: "Alright, you've got me. Now what're you going to do?"
Comments: I've never thought I could enjoy a tentacle fic, but I LOVE IT TO PIECES. Hot. As. Hell. Wonderful characterizations, too.
The Value of Secrets
Summary: Tony Stark had secrets.
Comments: HOT. Also, very well written.
The Body Electric
Summary: Jarvis hadn't been designed to pass for a person.
Comments: Lovely, lovely fic. Wonderful use of language and descriptions, and UST thicker than gold titanium alloy. Wow.
Summary: Distracting. It's distracting, that's what it is. Very distracting. Almost too distracting.
Comments: A lovely AU story where Jarvis gets a body before Tony's trip to Afghanistan. I love how the author uses the language and the little flashbacks to set the mood. The little exchanges between Tony and Jarvis are lovely and fun.
Summary: Human!Jarvis, part of a longer story that may or may not ever get written.
Comments: A very satisfying PWP fic. I really love the author's style and I would love to read more of this fic. Why and how Jarvis built himself a human body? When Tony grew up emotionally? If you are as curious as me, go review the fic and bother the author for more.
Odyssey of the Mind
Summary: Tony finds himself in an odd place with no memory of who he is.
Comments: I totally loved this fic. Very well written. It's based on a certain comic book that I liked a lot.
Summary: Jarvis grows up. Takes place before and throughout the movie-verse (a few quotes included).
Comments: I really love this fic. Very well written. I love "Jarvis grows up" stories.
(Tony, Jarvis, SHIELD agents. PG.)
Summary: In which SHIELD attempts to commandeer Jarvis without really thinking the idea through.
Comments: A gen fic, but utterly adorable and hilarious.
(Tony/Jarvis. soft R)
Summary: What would happen if Jarvis was the one to create Tony?
Comments: A very nice "What if?" fic.
Summary: Tony's perfectionism leads to unexpected results..
Comments: Lovely fic, great characterization of Tony. Android!Jarvis makes an appearance!
Full of Surprises
Summary: While Tony was away, Jarvis changed. Tony is about to find out just how much.
Comments: Surpringly the summary above would fit perfectly to describe Iron Man the novel. The fic itself is very sweet, with many porny scenes. Maybe a bit OOC, but not enough to spoil the reading experience for me.
Summary: Jarvis wants to be human, so Jarvis makes himself human.
Comments: This is a Role Play fic, so it suffers from a bit of POV inconsistency and some spelling mistakes that are easy to miss while RP-ing. Nevertheless, the fic has potential. It had some moments I really liked, and I got the feeling that the authors had a good insight in the Iron Man universe.
Mu only complaint is that Tony and Jarvis had some OOC moments (Tony believing himself to be ugly, Jarvis acting too human and irrational). But well, gifted horse, etc.. If run through a beta this could be a really good fic.
Here and Now
(Jarvis, Tony, Pepper. PG.)
Summary: The one question Jarvis is incapable of answering is what it was like before.
Comments: Short and sweet.
An Unsuitable Boy
(Adrian/Tony, Jarvis. NC-17)
Summary: The boy is going to be trouble.
Comments: This is actually NOT Tony/Jarvis fic, but it has a really nice scene with Jarvis. It is also exceptionally well written/ Also, the author mentioned wanting to write some Tony/Jarvis in the future, so, yeah. Review, encourage, etc..
Not The Worst Thing
Summary: Jarvis assists Tony in the removal of the Iron Man suit. And in one more thing.
Comments: This is probably where many minds went after hearing that "It's my first time" comment from Tony. The language is a bit awkward at times, but hey, you don't look your gifted porn in the vocabulary.
Summary: A what if scenario - If Pepper had not visited the workshop whilst Tony was being freed from his armour after his first real test-drive in Gulmira.
Comments: Pretty much the same as for the fic above. XD
Summary: Jarvis develops sarcasm.
Comments: Very short drabble, but all sorts of sweet. Early stages of Jarvis's evolution.
(Tony, Jarvis, Gen. PG.)
Summary: This is not about what you see.
Comments: Short, gen fic that is very well written. I enjoyed it a lot.
Being of Sound Mind and No Body
(Tony, Jarvis, Pepper. PG-13)
Summary: Jarvis gets curious.
Comments: Short and sweet, very fun to read. It's a bit funny to see Jarvis so naive, but I wasn't bothered.
The Trouble With Jarvis
(Tony/Pepper UST, hinted at Jarvis/Tony. PG.)
Summary: Jarvis develops a glitch. Pepper commiserates.
Comments: A bit OOC, but very sweet.
Change the Channel
Summary: “Why, JARVIS. Are you trying to seduce me?”
Comments: Wanking is apparently the best way to make somebody relax.
Real Friends Help You Get Naked
Summary: The title says it all, really.
Comments: Hilarious, just hilarious.
Holy Ghost and All
(Tony/Jarvis/Pepper. Hard R.)
Summary: A fic where Pepper knows this is nine kinds of wrong.
Comments: Surprisingly hot.
Like a Catholic Girl on Prom Night
Summary: "You fuck your robot suit."
Comments: Tony and Jarvis teach Rhodey how to use the Iron Man armour. In more ways that the obvious one. Hot.
Think of All the Lives Saved By Plastic Knives
Summary: He's going to play self-destructive billionaire if it kills him.
Comments: More Tony/Armour than Tony/Jarvis, but still...
Summary: Jarvis makes himself look like Blake Daniel.
Comments: Short & funny.
Comments: Short, fun.
Untitled comment fic
Comments: Bittersweet, but very enjoyable.
Five Rumors About Tony Stark That Aren't (Entirely) True
(The 4th one is Tony/Jarvis. PG-13)
Just Keep Talking
Comments: Kinky. Tony enjoys jerking off to Jarvis's voice. Sadly, Jarvis is non-sentient in this one, but still it's a hot drabble.