I think the answer depends on the lender but in general here is how I understand the requirements from my own personal experience with my two rental properties.
To count the income from a rental you either need to have a two year rental history OR if you have minimum amount of equity (I believe it is 25%+ but a lender would need to verify) then you can count up to 75% of the monthly rent.
Most lenders are also going to want you to show that you have atleast 6 months of reserves (monthly payments and HOA dues) for all of your properties in reserves in addition to your down payment.
Again this is just what I remember from my own personal purchase experience last year. Requirements may have changed since my purchase and may certainly vary depending on loan type and lender.
If you need better more exact answers, I would be happy to put you in touch with the lender I use.
Allen Tate Realtors