Note that "island of stability" means different things to different people. If you just look at a table of isotopes, there is a very clear "strait of instability" beyond the doubly-magic lead-208. In that picture, all of the actinides (e.g. uranium) live on an "island of stability." Those elements are produced in kilonovae; kilonovae are responsible for a substantial fraction of all elements heavier than iron.
Source, key, and other data; generally darker squares denote longer-lived isotopes.
An open question is whether there exists a second "island" of even heavier elements whose lifetimes are "long." There is an illusion of such an island in this particular figure due to missing data for neutron numbers in the range $160 < N < 168$. However, of those superheavy isotopes which have so far been observed, the trend seems to be that the longest lifetime for a given mass $A$ only seems to decrease as $A$ gets bigger.
The absence of any geological evidence for a second, superheavy island of stability probably has more to do with the maximum lifetime of any of its hypothetical members than with whether such heavy fragments are produced by kilonovae. Even for the actinides, there are only three "primordial" isotopes with lifetimes comparable to the current age of the Earth; all the others occur only as decay products or in transmutation laboratories.