Lenders look at credit first, income second, the asset next. If your income is part time, chances are it isn't very much. If its part time and short time, which many part time jobs are, they will have a hard time expecting it to be permanent enough to rely on.
Hard money lenders are also called equity lenders. They want a lot of cash into the deal and the rest of the deal has to make sense. They charge higher fees and rates than conventional or portfolio lenders. You have to still show them you have the capacity to pay them back. Hard money loans are also typically short term, so you'll need to have permanent financing lined up in 3-6 months in many cases.
Adding that this is likely to be a non owner occupied property only makes this more complex. NOO loans generally require 25% down to start and they still want the income and assets to make sense.
You can talk to some mortgage brokers; ask if they have portfolio products which offer different guidelines than conventional. I'm not aware of any way to do what you are asking, but that doesn't mean it doesn't exist.
Decide a few details before you proceed though. Will you live in it or not? How much will you put down and what will you have in reserve? Can you go to full time employment or get a second part time job?