As a Realtor I have knowledge of your question. Lender underwriting criteria is constantly changing. In short I believe you can find a lender who will look at "landlord" experience differently than a two year waiting period.
An example would be if you have at least 25% equity in your current home. If so and you can provide lender with a copy of a lease and a security deposit from tenant and can naturally meet credit/income/debt criteria, you can qualify for a mortgage without being a land lord for two years.
If you like I can put you in touch with a mortgage broker who can help you.
Further, in order to have real estate qualify as an investment property, it must be shown on a tax return as such. (Enacted in 2011). This is where the banks will look to qualify income as supporting your financial picture. So that will mean that at least a year will need to pass. Also, remember, only the "net" will help you here.
Answers are, of course, not just this simple. You may be missing another opportunity all together. I am licensed in both New Jersey and in New York. Feel free to contact me if you want to discuss this, or any other future investments, whether in New Jersey or in New York, whether residential or investment/multifamily/mixed use commercial, or the like, in greater detail.