I want to make my meteorite hit the Earth, after which the impact debris and ash blocks the sun just enough to make agriculture no longer feasible.
Recent computer simulations and atmospheric models indicate that within a few weeks to months temperatures and light levels would have begun to rebounded [sic] due to the release of heat stored in the oceans and the coagulation and fall of the dust and soot. The major effects of the dust and soot would last about 1 yr [sic] or less.
You could get more dust and soot by using a bigger rock, but I don't think the time the impact winter would last would scale linearly with thr asteroid size or mass. A big enough impactor might actually trigger another Hadean, so you'd be swapping a big problem for an impossibly bigger problem.
Even with just one year of impact winter, the dino killer caused so much collateral damage that another one would kill us all from the heat alone, and then there are the quakes, tsunamis, and kinect impact of the ejecta.
Your best bet for a permanent dark cover is manmade pollution or some biological process, not an asteroid or comet.
There is nothing that a meteorite could be made of that would do that. But it's not necessary. You see, all it really takes is for the cold to last long enough that the ice has time to significantly spread. Once that happens with more and more of the world coloured white, more sunlight will be reflected back into space. This increase in "albedo" will lead to an ice age.
Consider the famines of 526 to 539 AD as an example. In this instance, a combination of volcanic eruptions and possibly impacts by cometary fragments caused global diminishment of sunlight. Crops failed, and civilisations trembled.
In order for such an effect to last for millenia, I would suggest that it would need to be caused simply by larger impacts.
Unfortunately, it is exceedingly difficult to model global atmospheric conditions in such a scenario, so there is little evidence to go on. However, it is possible that impacts on the scale of chixulub might take millenia to fully recover.
This is especially the case in that most photosynthetic organisms on Earth would be killed by such an impact, with recovery beginning from seeds and underground roots and tubers. Human survivors would likely accelerate the process once agriculture becomes viable again by planting stored seed resources.
A suggestion I might make, is that perhaps the Earth is struck periodically by fragments of an object that are crossing the planet's orbit? If smaller impacts are occurring repeatedly on a yearly basis, they could perhaps maintain particulates in the atmosphere?