CWAD centre manager Julie Blackley said she wanted to raise awareness of the difficulties after receiving more than 100 complaints, with a further 190 lodged since to make nearly 300 complaints in total.
"We need to make a stand," she said. "Enough is enough. It's not fair for the deaf to suffer.
"People get foreign translators straight away and that's beautiful, that's a beautiful service for them. For deaf people, there's just barrier after barrier."
A spokesperson for University Hospitals Coventry and Warwickshire NHS Trust (UHCW) said the trust was committed to providing accessible services for all patients, included those who use BSL, and 98% of bookings through LanguageLine had been fulfilled.
"However, we are sorry to hear of the experience some patients have shared about their needs not being met whilst in our care," they added. "Every patient deserves to feel respected and safe in our care."
The trust said it was set to engage and consult with local deaf and community groups to address issues and welcomed the opportunity to "listen, learn and improve" its services.
A spokesperson for LanguageLine Solutions said the company was pleased to engage with the association to identify the challenges they have faced.
"We will continue to work closely with UHCW to improve services and ways of working, resulting in a more consistent level of support for deaf and deafblind patients," they said.