if by bilennium you mean 1024, i suggest a different neologism, since that one's already taken for 1,000,000 years.

kilo = SI prefix for 1000
kibi = invented prefix to mean 1024 in attempt to avoid confusion over how to interpret 'kilo' in a computer-memory-size context

So: kibinnium

Whose spelling we might as well alter to 'kibonnium' just for completeness.