Trying to apply in practice the theory of finding the optimal price in a cournot competition
Suppose you are willing to believe that the demand curve has a constant elasticity $\epsilon$. Then the optimal price $P^*$ is given by
$$ P^* = \frac{|\epsilon| \hspace{0.1em}c}{|\epsilon|-1}$$
where $c$ is the marginal cost of producing gold rings (assumed constant). So if your friend can estimate the elasticity $\epsilon$ (e.g. by randomly varying the price and seeing what happens to the number of rings sold), they should be able to estimate the optimal price.
To illustrate, suppose that your friend thinks that increasing the price by 1% will decrease demand by 2%. Then $\epsilon \approx -2$, i.e. $| \epsilon | \approx 2$. The formula then proposes charging $2c/(2 - 1) = 2c$; that is, a 100% markup on the constant marginal cost.
As an aside, note that this formula holds independently of the market structure. So you don't need to worry about whether the market is described, say, by the Cournot model (except insofar as this bears on your estimate of $ \epsilon$).