Do rising CO2 levels change the appearance of the sky in infrared?
Due to man made climate change, from space, the Earth currently looks a little darker in Infra-red (IR) and a little colder (longer wavelength), but the change is small and would be hard to notice without sensitive photon-counting equipment.   The earth doesn't exactly glow in steady color in IR either, it swirls and looks like a circulating, 100% cloud covered planet, which makes sense when you consider that our atmosphere, mostly the H2O and CO2 in the atmosphere is opaque to much of the infrared spectrum, so it looks a little like Venus in the IR, but not quite as dense with clouds.   What's more, you'd see seasonal variations and day/night variations, so it would be hard to notice a pretty small climate variation over that.   

See YouTube video and article of the Earth in IR: Planet Earth in Infrared (Synchronized)

and the article: Our Planet Has the Vapors.

The video isn't quite right, because it's only one wavelength designed to track water-vapor not the entire IR spectrum, but I thought it was close enough to use as a starting point.

The short answer is, at least for now, the Troposphere is warming but the stratosphere is cooling and contracting, so from space, in IR, Earth is both a little smaller and a little colder/darker, at least, for now.

The longer answer is that when the Earth is in energy equilibrium, that is, not undergoing climate warming or cooling, the Earth gives back to space  the same amount energy it receives from the Sun, at least, more or less.  There's some variation, but it's largely the same.

The only way Greenhouse driven warming can happen, is for the Earth to hoard heat, and gives back less heat to space than it takes in from the sun.   When the Earth grows colder, it's the opposite, the Earth needs to return more energy to space than it takes in from the sun.  This variation doesn't have to be all that big, for example, a fraction of 1% variation over enough time can be enough to start or end an ice age, but that's the only way warming or cooling can happen.  It has to be an imbalance in Earth's energy equilibrium (technically, also, it could be a change in Earth's orbit or a solar minimum), but Earth's orbital changes take tens of thousands of years and Earth's climate changes mostly take 1,000 or so, and solar minimums are relatively weak and thought to only last a couple hundred years or so.  So the primary driver for climate change, warmer or colder, man made or natural, is the Earth hoarding or losing energy.

This doesn't have to happen entirely in infrared.  Changes in albedo/reflection can play a role too, for example, as snow cover and permanent glaciers grow, the visible light reflected off earth gradually but steadily increases resulting in the Earth giving back more energy than it takes in, leading to a cooling, sometimes an ice age, and the energy imbalance continues until the Earth is sufficiently cooled to reach a new equilibrium.

Currently, the Earth is hoarding heat and it's albedo is relatively unchanged, meaning that it's giving back less IR into space than it used to, so, in IR, the Earth looks a little bit darker than it used to before man made climate change.   Ballpark, about 1% darker in the IR.   As to changes in color, there's some variation in wavelength on both warmer and colder, but on average, slightly colder/longer wavelengths.  

Estimates vary, but, ballpark, Earth is trapping roughly 2 extra watts of energy per square meter due to climate change and most of that trapped energy/heat goes into the oceans, very gradually warming them.  The lower atmosphere is more effectively absorbing and reflecting thermal radiation from the surface so less IR is reaching the upper atmosphere and less is going into space, so while the surface of the Earth does grow brighter in IR what is mostly seen from space is the cooling upper atmosphere.   

Over time, as the Earth's surface and lower atmosphere grows warmer, it will emit more IR and the upper atmosphere will, in time, give back into space just as much IR as it used to before climate change, and probably more, but that will take 100 years or so, perhaps longer.   Also, as Earth's ice cover drops and it's oceans rise, Earth's albedo will mean less visible light is being reflected into space, so the thermal radiation will need to increase to make up for that.  So, in a century or two, the warmer Earth should glow brighter in IR and on average, a bit warmer/shorter wavelength, too.   How much will depend mostly on how much ice cover melts, but we're probably not looking at more than maybe a 1% increase, 2% tops.

For some numbers and pretty charts, see here.

Earth is hit by about 340–341 watts per square meter of energy from the sun, that's on average, summer/winter, equator/poll and night/day.  Direct sunlight on a perpendicular surface to the Sun's rays is about 4 times that.

Of that 340–341 watts, currently about 29% or 100 watts is directly reflected back into space as mostly visible light.  The remaining 240 or so watts (per m2) leaves the Earth in the form of infra-red or thermal radiation.

About 170 watts of that 240 comes from the high atmosphere.  About 30 from cloud tops and about 40 watts from surface radiation.   While the Earth's surface does grow warmer during climate change and brighter in IR, 90% of that gets re-absorbed by or reflected back by the atmosphere and only 10% reaches space, so the added brightness you might expect to see off the warmer surface makes up only a small part of the total.  

If we say the Earth's surface has warmed about 0.8 °C, say from 288K to 288.8K, using the 4th power rule, that should emits about 1% more thermal energy than it did before climate change, but 1% of 40 watts comes to about 0.4 watts per square meter increase, and perhaps decreased overall due to the more opaque atmosphere with higher CO2.   The biggest factor for the earth's IR image is the temperature of the upper atmosphere. 

As an FYI, there are other imbalances to the heat in/heat out equilibrium equation, for example, a really big volcano might release enough heat into the surface to unbalance the ratio temporarily and following a big volcano there's an increase in the amount of light reflected off earth which leads to a relatively rapid but temporary cooling.   A large enough meteor impact could also create a variation, and the Earth is hit by solar wind and cosmic rays and it loses some heat in very fast moving particles that exceed escape velocity (mostly hydrogen from water molecules).  The Earth also has internal heat coming from it's warm interior, which means the Earth does emit a bit more heat than it receives overall, at least on average, which does throw off the expected equilibrium a little bit.  

And, final and curious sidebar, you might ask, how the Earth's surface can emit 400 watts per square meter, which is more energy than Earth receives from the sun.  That has nothing to do with your question though, but it's a curious statistic I think.   It's because our atmosphere acts like a blanket, warming the Earth overall.

Hope that wasn't tl;dr.