As Russ points out, the orifices and clearances required to make an injector that small would put a pretty severe test on the fuel fitration system, to say the least.
Then, as any steam or IC engine modeler will tell you, fluids don't scale. . . the 'minor' condensation that happens in a steam pipe between the boiler and engine in a full size engine (say 6" bore) will cause knocking in a (1/4 scale) 1.5" bore and completely prevent a (1/8 scale, 0.75") bore engine of the same design from even rotating. And the smaller the engine, the larger the surface area is compared to the swept volume, increasing the condensation rate, and compounding the problem.
Going the opposite way, for a model diesel, the heat in the compressed air in a small cylinder is going to escape to the cooling medium (or even the piston and valves) much more readily than in a full-size engine-- Solutions are left to the reader.)
Similarly, in a model internal combustion engine, the fluids fight you; a droplet produced by a carb venturi or injector spray that would work exceedingly well for a full-size engine, might not even ignite, let alone burn completely, in the time and mean free path available in a model combustion chamber.
So even if you managed an injection pump in 1/8 scale, you would still need to atomize your fuel much finer than even the newtech high-pressure, common rail engines do. . . A tricky problem for a hobbyist.
(And that injection pump and injector? not as easy as you might think in any scale- A retired Caterpillar engineer tells me that the injectors from the 50s and 60s had critical dimensions with clearances in the 0.000x" range and tolerances in the 0.0000x" range (I don't even wanna guess what the numbers are like now). Now scale that down by a factor of, oh, say, 10, and you're trying to machine (on hobby equipment!) multiple parts fit each other within millionths of an inch. . . . Yeah, Ok, we're talking a model here; it doesn't have to last 10khours between major overhauls, doesn't have to meet EPA or market-driven fuel efficiency and pollution targets. . . it still has to run reliably enough, long enough, to get a video of and show off to your friends. . . so you've still got to get those clearances pretty close to right.)
I don't recall any true diesels (those with injection pumps) below about the 300CC/ 15 CID level- your Davis diesels and other compression-ignition engines are more in the line of semi-diesels or hot-bulb(hot-surface) engines that mix air and fuel before compression.
(which is not to say that it hasn't been done; just that it's not commonplace)
However, there are a number of operable, multi-cylinder, 4-cycle, spark ignition gasoline engines with bores and strokes of 1/4" and less out there. We're talking about radial engines with that would easily fit and operate inside a coffee mug.
So you might find that a model spark ignition is far easier than an injector pump; even if the coils and such don't scale any better than the fluids.