I have done this in the past with cast cement reliefs, for a quick fix the trick is the same one that antique restorers use to forge aged furniture, picture frames etc.
first make sure to use a powder that doesn't stain; for white it is usual to use pumice, for black fine carborundum powder (can be bought by the kilo from Glasplies.
http://www.glasplies.co.uk/fibreglass-supplies/filler_powder
Then you need to find a suitable tacky liquid that will not make a permanent coating on the 'proud' parts of the relief. the idea is to scrub the liquid into all the recesses, then wipe it off of all the proud surfaces, even let the wiped bits dry off a bit - then while the liquid in all the crevices is still sticky pour on powder (just like sprinkling glitter onto christmas decorations). the liquid doesn't need to be all that permanent as the grit in the crevices will accumulate more natural grime by the time the 'glue' has dissappeared.
for really fine work like gesso or revacryl plaster (yes a casting plaster that survives outdoors) i have used ordinary wax furniture polish (it weathers away from the proud surface in a couple of weeks) also sanding sealer (shellac & meths). For coarser cement castings I have used a diluted pva (a waterproof one like resin w waterproof - so it doesn't go white in the rain).
I have also seen this done by premixing the non-staining grit/powder with the liquid and then applying and removing the stuff as required, but personally i think it encourages you to shade in areas and can give a really false look.
The process involves a different approach to painting, you are only falsifying the beginning of an ageing process - where you apply the grit, more stuff will adhere quite rapidly (and yes yoghurt really does encourage a patina). ideally the sticky liquid that you use will weather away from the proud surfaces quickly enough that they look aged too, not leave a coating of any sort, and definitely not staining anything, that is why you should avoid any pigments or very fine powders.
Another, more risky approach is to mix a fine slurry of the same cement, but replace the sand/finest agregate with a non-staining dark powder. increase the powder until you have the right shade - don't worry if the mix is way too weak in cement. Soak the cement surface with water then scumble this slurry into the relief making sure that it is very thin on the proud surfaces. wipe away what you can with a cloth/scourer/wire brush while it is still wet. Then when it is cured, wipe the thing over with cement remover/etching fluid a few times to cut away the surface to expose the cement beneath. make sure to wash away the etch with each application though or it will decay the surface.
be careful to use the same cement, so if have used white opc possibly with a bit of pigment, use the same (the cements should match, the agregate darkens). It can be tempting to use ciment fondue for its gorgeous dark grey colour, but it really disagrees with opc and will flash set (though that could be usefull too).
Writing this made me wonder if you could soak the object in water and then blow ciment fondue dust onto it evenly, to make a really thin surface coating, then etch that away with a rag. I must give it a go.