At 22.65 g/cm³, I suppose that you could do that at similar expense. Although because there would be a negligible increase in pellet mass, I doubt that there would be a noticeable, let alone measurable increase in penetration depth over that produced by pellets made of iridium. The increase in mass for a 00 Buck pellet made of osmium would be on the order of ≈½ grain.
If you really want an ''exotic'' substance, there's the synthesized element 271Hassium with a half-life of ≈10 seconds (due to α decay) with a interpolated mass-density of 40.70 g/cm³. Only a few atoms of 271Ha have ever been synthesized. However, if there was ever enough 271Ha to accumulate into a 00 Buck pellet, it would weigh in at a rather hefty 193.7 grains.
At the same proposed velocity of 1,212 fps in the other examples above, the predicted terminal penetration of a 00 Buck pellet made of 271Ha would be—
mTHOR: 64.13 inches
Q-model: 74.13 inches
MacPherson: 77.52 inches
By comparison, gold would be a much cheaper option even at today's value of $1,800 - $2,000 per troy ounce.