Federal student loans, grants, or any federally subsidized assistance is not available for those under Deferred Action.

You can look into scholarships provided for dreamers, a simple search will bring it up.

There are also private loans, as you mentioned, available. Every major bank does student loans, I would recommend Discover or Wells Fargo.
(e.g. Wells Fargo does loans up to 25,000/yr and with a 4.00% APR you could be looking at $184.92/mo for 15 years).

Of course, the terms of the loan are topics to discuss with the bank, but as with any loan you'll need to show/establish a credit history. If you have no/limited history, getting a co-signor will help.