You can prepare chemical solution of your nanoparticle e.g. 1 mM Au solution. Add desired amount of ZrO2-Y2O3 powder in this solution. Heat it till its boiling temperature and then add the reducing agent. It will result in the reduction of Au nanoparticles and eventually would give you Au coated ZrO2-Y2O3 powder. This is one method, you can also find some other methods from the database.

Good luck!

Here are 2 approaches I would personally employ if I were in your position

1. I am assuming that all the phases within the zro2-y2o3 system (regardless of their composition %) are insoluble in aqueous solution. and that your nanoparticle of interest is water soluble.

Not all nanoparticles are the same, coating the surface of zro2-y2o3 with gold nanoparticles is VERY different to doing something like attaching TiO2 or CdSe 

Develop a clever short chain hydrocarbon which has the form X-C(n)-Y where X and Y are end groups that react to:

X=zro2-y2o3

Y=nanoparticle

n=long enough such that charge repulsion>radius of gyration but short enough such that the statistic probability of the end group 'seeing' your zro2-y2o3 is viable

2. Another possible method is to try to create a self assembled monolayer. I am assuming that the zro2-y2o3 exhibit negative static charge, I would try to aerate the negatively charged powder in a vortex while introducing positive nanoparticles into the gaseous 'solution'.

these methods create systems with different adhesion forces which are useful for different applications. I think more detail in the question would help researchgaters to give a more formulated answer.

Incipient Wetness Impregnation is a well known and well researched method.  It is well described especially in the patent literature for Fischer-Tropsch catalysts.  Essentially, you add a solution of (usually) a nitrate salt of the metal or metal oxide to a collection of the substrate powder just to the point where adding any more would result in visible free standing liquid.  Dry the mixture in an oven.  From here what is generally described is a slow oxidation of nitrate in flowing air or oxygen in a tube furnace - slow ramp rate, and sufficient time at the right temp. for you're system.  You will likely notice the brown effluent of nitrogen dioxide at some point.  Its a good idea to bubble your effluent through a beaker of oil. This will produce particles of metal oxide on your substrate.  But if you want metal particles, you will need to reduce their oxides at elevated temp. Under flowing hydrogen - of course this step will only work if the free energy of formation of the oxide of your metal of interest is smaller than the free energy of formation of your substrate oxide or your substrate will be reduced to metal as well.