One of my favorite movie quotes comes from The Hunt for Red October.
"Can you launch an ICBM horizontally?"
"Sure, why would you want to?"
You didn't tell us anything about your motor, but let's assume a reaction engine of some sort mixing oxygen with fuel to get a resounding Bang! I kinda suspect it needs to be non-nuclear as a nuclear engine would have the tendency to, well, atomize anything you might use to create your smoke trail.
Therefore, it's a trivial matter to introduce an additive to color the smoke. Technically, any additive used today could be used with your rocket so long as enough of it is used. Rockets tend to have really, really, really big engines.[Citation Needed]
But there are some problems...
In an atmosphere, there's something to kinda hold all the smoke together. The exhaust pressure dissipates and eventually equals the atmospheric pressure, after which the smoke moves with the wind. In space, this doesn't happen. The velocity of the exhaust (inevitably greater than the velocity of the rocket) forces the smoke to keep on truckin', and that usually in a lot of directions. I therefore expect the cloud to dissipate very quickly, necessitating an unholy amount of additive.
Unless you have spectators with really powerful flashlights (obligatory XKCD), the smoke could only practically be seen from the sun-side.1 So I question what the purpose of this exercise is? As smoke moves off the spherical plane defined by sunlight, it's efficiency drops. In other words, it has much less effect than it would inside an atmosphere.
In the words of Douglas Adams, "Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space." The distance between spectators and jet planes is trivially insignificant compared to space, so unless you're doing this for someone outside a space station in a very slow-moving rocket... yeah, another frame challenge.
So, I believe it can be done (emitting smoke in space), even using the same materials used by Jet Planes today. But I question whether or not it would be worth it.
1 Light scattered through the smoke might allow it to be seen somewhat from the "dark" side, but considering you're looking into the unfiltered glare of a star, it might still be hard to see.