RNZ reports one motion was withdrawn and another ruled invalid due to their lack of support in the 52-seat parliament.
Proposed constitutional amendments would change the rules for filing no confidence motions that have defeated five Vanuatu prime ministers over the last 20 years.
However, the analyst Dr Tess Newton-Cain said the two failed motions represented valid concerns of backbench MPs.
"They were an attempt to capitalise on what is an apparent concern among certain back benchers that they are not being sufficiently included in government decision making. It would certainly appear that some of that concern, if not all of it, but some of it certainly is valid," she said.