  Blazars constitute the vast majority of extragalactic $\gamma$-ray sources.
They can also contribute a sizable fraction of the diffuse astrophysical
neutrinos detected by IceCube. In the past few years, the real-time alert
system of IceCube has led to multiwavelength follow-up of very high-energy
neutrino events of plausible astrophysical origin. Spatial and temporal
coincidences of these neutrino events with the high-activity state of
$\gamma$-ray blazars can provide a unique opportunity to decipher cosmic-ray
interactions in the relativistic jets. Assuming that blazars accelerate cosmic
rays up to ultrahigh energies ($E>10^{17}$ eV), we calculate the "guaranteed"
contribution to the line-of-sight cosmogenic $\gamma$-ray and neutrino fluxes
from four blazars associated with IceCube neutrino events. Detection of these
fluxes by upcoming $\gamma$-ray imaging telescopes like CTA and/or by planned
neutrino detectors like IceCube-Gen2 may lead to the first direct signature(s)
of ultrahigh-energy cosmic-ray (UHECR) sources. We find that detection of the
cosmogenic neutrino fluxes from the blazars TXS~0506+056, PKS~1502+106 and
GB6~J1040+0617 would require UHECR luminosity $\gtrsim 10$ times the inferred
neutrino luminosity from the associated IceCube events. Blazars TXS~0506+056,
3HSP~J095507.9+355101 and GB6~J1040+0617 can be detected by CTA if the UHECR
luminosity is $\gtrsim 10$ times the neutrino luminosity inferred from the
associated IceCube events. Given their relatively low redshifts and hence total
energetics, TXS~0506+056 and 3HSP~J095507.9+355101 should be the prime targets
for upcoming large neutrino and $\gamma$-ray telescopes.
