IPA: /ˌʌn.bɪˈliː.vɪŋ.li/
KK: /ʌnˈbɪlivɪŋli/
In a manner that shows doubt or disbelief.
She looked at him unbelievingly when he told her the news.
Unbelievingly → It is formed from "un-" (meaning not), "believe" (from Old English "beliefan", meaning to have faith or trust), and "-ingly" (a suffix used to form adverbs). The word "unbelievingly" means in a manner that shows a lack of belief or faith.
Think of 'not' ('un-') having 'faith' ('believe') and doing so in a way that describes how you act ('-ingly'). This helps you remember that 'unbelievingly' means acting without belief.