[miked17]

Can anyone give me some arguments as to why Osmium and Iridium are so dense, or, according to said arguments, which should be denser?

 I know period 6 transition metals experience the lanthanide contraction and relativistic effects of their inner electrons which would make their electron clouds tighter and 'harder', but beyond that, I can't really think of a good reason for the density of these two metals.

[ATMyller]

It's more like a sum of things. Small atomic radius, due lanthanide contraction, heavy nucleus and tight crystal structure result in high density.
According to experimental data osmium would have a slightly higher density, but calculations based on space lattice's give a bit higher density for iridium. Altought the diffrence is too small ( < 0.2% ) for any conclusive results.

[mdlhvn]

d=m/V

In general, you should focus on mass (m) and volume (V) to explain the density-increasing phenomenon of lanthanide series. And while m does not change so much, the explaination due to V is reasonable.

In my opinion, the reasons miked17 give are enough.

You can find more on Wikipedia

http://en.wikipedia.org/wiki/Lanthanide_contraction
http://en.wikipedia.org/wiki/Osmium