Employers see unexplained holes of non-activity (and that's not just not working, that's not working and not doing anything productive to fill the time either) as red flags. And lying over something like this (you weren't in prison or anything) isn't worth it.
Long-term unemployment is perceived much worse than slight overqualification. I mean, 9 months could just have been an internship. If you're applying to internships they may not hire you because of this, but otherwise I don't see a problem.
So I think it is better to just write it down.
They may not hire you because you're overqualified and they want to pay the employee a low wage, so they wouldn't want someone with more experience who will fly away from the job he's overqualified for as soon as he can.
I don't think the fact that you have 9 months of experience would be considered as something that makes you too hard to train (as opposed to a 50 years old programmer who didn't keep his knowledge up-to-date).
Whether they would prefer a fresh graduate over you depends on their reason for looking for a fresh graduate, but I think it's possible.
There's also the issue of why your previous employment lasted only 9 months though, just hope you can get to the point where they ask you that question (unless you were fired). Disregard this if it was an internship.