How to avoid and address a lack of gender diversity in grant proposals?
This is a hard and important problem.  There are a few things you can do to address it.
First, admit that there is a problem indicated by the demographics of your discipline.  Tell the funding agency that

neither of the institutions involved have female staff eligible for the grant scheme working in the area of our proposal.

Tell them briefly about your universities' plans for future diverse hiring.  Tell them that the grant applicants do not have control over the diversity of current staff (if this is true).
Explain how the project will contribute to gender inclusivity.  You said you plan to hire one postdoc.  How will you encourage gender minority scientists to apply for that postdoc?  How will your selection process prevent discrimination?  How will that postdoc receive professional development that will advance their career?
Will you be communicating about your project to the public, and will that be done in a way that reaches people of all genders?
It sounds like your project is applied.  Will the application benefit gender minorities?  Even if they get a minority of the benefit, it's still worth pointing out that your project does not exclusively benefit one gender.
Do not add a token applicant.  You are obligated to allocate the project funds efficiently.  Some people argue that tokenism has the opposite of the intended effect.