Answer
It is probably not diamond.
Work Step by Step
We divide the mass of the jewel by the fraction of the density underwater. Thus, we find:
$ = \frac{5.4 \times 10^{-3}}{1-\frac{3.51}{1000}}=.005$
This corresponds to an apparent weight of $.005 \times 9.81 = 5.3 \times 10^{-2} N$. Thus is in the realm of $3.2 \times 10^{-2}N$, but it is not the same, so it is probably not diamond.
