It depends, what are the advertised hours? If it's being advertised as a full time position and you are definitely not prepared to do that then I think yes mentioning what you are prepared to do is a good idea. If you are proposing a job share are you hoping someone will materialise from other candidates who can do the right hours to fit in with you? Alternatively they'll need to do a whole new recruitment campaign to find someone suitable to fit in.
I see you are on a tight deadline and are already working there anyway. I'd be inclined to say in your cover letter that you are hoping to work part time and would be very happy to discuss options that might work, including the possibility of a job share. That way you sound positive, proactive and flexible. Then follow up with a discussion with the relevant person if that's appropriate which it might be in your case.