This presumes you're desperate for work, those that get stuff done have no problem, they approach the business forthrightly and tell them this is what I'm working on, and I want it to be mine. If a business has an objection to a person owning the rights to their work, then you can tell your signing up for indentured servitude rather than employment. It's not a place you want to work for anyway.
I used to have this attitude as well that I couldn't ask for stuff and no one would agree, I gave it up, started approaching things earnestly and honestly and it's amazing the things people will do if you ask them in a respectful and polite manner.
It depends who you are. If you're an established software engineer with a name, sure. If you're a 22-year-old out of college, no chance. Most of us are between those extremes, of course, and generally realize at some point that we've moved into the with-leverage crowd. But nobody starts there.
I actually think it's best, as a general principle, not to work on side projects while employed. If the side project really is a side project (i.e. it's unrelated to your work and therefore something you justly own) you'll do a much better job of it if you work on it full-time. The side project and the day job usually both suffer if you try to serve two masters. But there are cases to which this principle doesn't apply (i.e. an iPhone app that doesn't take much time to build but becomes very popular) and it's for those that we need (in NY) better laws.
I used to have this attitude as well that I couldn't ask for stuff and no one would agree, I gave it up, started approaching things earnestly and honestly and it's amazing the things people will do if you ask them in a respectful and polite manner.