  The discovery of ultra-high-energy neutrinos, with energies above 100 PeV,
may soon be within reach of upcoming neutrino telescopes. We present a robust
framework to compute the statistical significance of point-source discovery via
the detection of neutrino multiplets. We apply it to the radio array component
of IceCube-Gen2. To identify a source with $3\sigma$ significance, IceCube-Gen2
will need to detect a triplet, at best, and an octuplet, at worst, depending on
whether the source is steady-state or transient, and on its position in the
sky. The discovery, or absence, of sources significantly constrains the
properties of the source population.
