unbelievable vs unconvincing

unbelievable and unconvincing both are adjectives.

Word	Noun	Adjective	Verb	Adverb
unbelievable	No	Yes	No	No
unconvincing	No	Yes	No	No

As adjectives, unbelievable and unconvincing are synonyms defined as:

unbelievable and unconvincing: having a probability too low to inspire belief

Other synonyms of unbelievable include improbable, unlikely.

unbelievable (adjective)	unconvincing (adjective)
beyond belief or understanding	not convincing
having a probability too low to inspire belief	having a probability too low to inspire belief