Hi, I’m from Thailand.
I just bought the rusty Fiat 850 Sport Coupe with no engine in the car. So I want to swap the engine but since it’s not a common car in my country, no one can answer my question. Even when I search the examples online, I barely find one. If anyone have done the swap for this car or anyone who have recommendations please tell me!
It’s not a common car in any country,
What would make you want to buy a 50 year old rusty car with no engine ?
843 cc (51 cu in) engine producing 47 hp, rear engine rear wheel drive
That’s problem #1.
Problem #2 will be finding a shop that can manufacture an adapter plate in order to mate a different engine to the Fiat transmission, assuming that this rusted hulk’s transmission is still in place.
It’s very possible that the OP will have to find both an engine and a transmission that will fit under the rear hood of this car. And then, there is the question of whether a different transmission would line-up properly with the Fiat’s drive axles.
In case the OP isn’t aware of it, this isn’t like screwing-in a new light bulb.
I would include problem #3, we don’t know what engines and transmissions you might has available to swap into the Fiat in Thailand.
The 850 is a rear engine, rear drive car with the engine mounted front-back much like an old Volkswagon Beetle. But the engine is an inline 4 cylinder. An inline 4, rear engine configuration is not common in 2021. A car with that confighration would be the easiest swap.
+1 to Mustangman’s comments, but I just thought of potential problem #4, which relates to just how rusty this corroded old Fiat actually is. If there is substantial rust damage to the chassis, it is possible that there wouldn’t be any safe way to drill/mount new motor mounts in the rust-damaged metal.
From afar, none of us knows just how much rust damage there is, but before investing any time or money on a replacement engine (and possibly a replacement transmission), the OP should have a qualified mechanic inspect the chassis in order to assess whether it is even possible to drill new holes to install new motor mounts (and possibly new transmission mounts).
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Have you searched for Fiat 850 forums (both coupe and convertible)?
I wonder if a Toyota FWD engine relocated to the back might work, much like Lotus does with the 2L Toyota engine.
Transverse inline 4 cylinder layout with the engine ahead of the transmission… replacing a longitudinal engine behind the transmission… I’m going to say that will be a BIG challenge!
He needs a longitudinal, rear engine layout as a replacement. The car is too narrow for almost anything else.
I do know of a project that is putting a Subaru AWD driveline backwards into a Fiat 850 Spyder (convertible) but that requires a complete re-engineering of the car and TONS of fabrication. Requires the creation of a back-bone chassis that can stand alone so the weak 850 body can be dropped on top and not need to support any loads. It has been really fun to see the progress.
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… and they probably started with a car that wasn’t riddled with rust.
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Why, YES, yes, they did start with a rust free car even though they are more than able to fix the rust.
It just isn’t worth it to START with a rusty car, ever!
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But, if that rust bucket is also missing an engine, it… somehow… becomes attractive to some people.
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And this engine is TINY! It’s an 850 cc (52 cubic inch) pushrod 4:
Almost no modern car engine is that small.
My college roommates had a 850 Spyder and a 850 Sports Coupe and even by the low standards of 50 years ago they were poorly designed, engineered, constructed underpowered, uncomfortable, unreliable and unsafe.
Of particular note, acceleration that was so anemic that I could beat the car on foot in a 100 meter dash, the electrical system was probably designed by Lucas after a dunken weekend, a swing axle rear that “jacked up” on turns even with bias tires and a high reving drive train built so cheaply that they even eliminated the oil filter.
On the plus side since they were frequently broken down with no parts availability and they rusted out faster than a damp steel wool pad, your chances of being killed was greatly reduced.
While the body design of the 850 Spyder was an attractive Bertone design, everything else about the 850 line was awful with no way to improve it.
How bad was it? It was outsold by it’s direct competitor, the MG MIdget which was based on a drvetrain designed in the 1930’s!
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not Lucas, but Magneti Marelli electrics… fits exactly your description in ALL but name! 
I’m sure you’re correct about that model, as well as most Fiats, but to my great surprise, the “Fiat in the woods” near my house has surprisingly little rust damage. Before Six Mile Run State Park became a park, that area was mostly farmland, and it appears that someone drove/abandoned the Fiat into what were originally open fields. Thirty+ years later, the area is forested, and anyone hiking through there is likely to be very surprised by this '70s era baby blue Fiat, hemmed-in by trees.
It has no engine, and it was obviously used for target practice over the years, but if someone could somehow haul it out of there, perhaps they might want to make a “project car” out of it.
The State Parks Department clearly has no intention of cutting down trees to extract it, so it will eventually just dissolve into the ground.
So far, this is the only pic that I can find.
This is the cryptic text that accompanies the photo:
Back up the hill, a blue metal surprise sits for eternity among oak, maple, and black cherry trees.
Personally I suspect that it drove itself there just looking for a place to die. 
but around here, closer to the port and distributors, similar 850 Spyders in similar conditions, turn up on a somewhat regular basis for practically nothing.
I’m reminded of the better mid engined X1/9 successor, which by that time were piling at the port and FIAT was trying to unload… The same darned problems, no parts, no support, no performance, literally rusting sitting on the dock and by that time hard to find any buyers even at fire sale prices.
My dealership, which was once the source for MGs, Fiats, and Citroens, reported that they used to have to resort to removing parts from recently-arrived Fiats in order to have replacement parts for other Fiats with valid warranty claims.
what about a VW or Porsche engine.
Seems like VW transmission is a viable option. The air cooled flat 4 has been installed. Seems like it might be too wide, but maybe not.
An early VW swap may be possible and in fact may he best solution but the car won’t be anything like the original Fiat.
Swaping a high reving little Italian motor for a solid VW flat four and entire rear end and the result is a VW dressed in drag. A Karmen Ghia or an early Porsche dressed up but with no substance and can’t dance.
The US concept behind the 850 was a lighweight body on a 850 cc engine to compete against the 1,250 cc MG Midget/Sprite and the 1,500 cc Triumph Spitfire which had their roots in the 1930’s but to do that with 30% lower displacement was a struggle.
Certainly the Bertone body design of the 850 Spyder was a major improvement over the Midget but to try to achieve the same power to weight ratio with 30% less displacemet was an exercise in futlity. You can only strip so much of the weigh out before it becomes like tin foil.
Of course we’ve all seen mini sports cars with powerful engines (the Alpine Tiger) but those were overbuilt chassis, not a lightweght frames.
So to the OP’s question, a replacement motor for a lightweight 850 which was designed for 50 hp, anything over that and you’re looking for trouble,
Even within that range the problems of swing axle “rear wear tuck”, elecrical problems and parts availability would have me running like a lttle girl.