Any way to refinance a rental home with no equity?

Check to see if your first loan is owned by Fannie Mae or Freddie Mac. If it is, and it was closed prior to June 2009 (not January, as originally indicated), you MAY be able to take advantage of a specific subsidized refinance program permitting no-equity and slightly underwater refinances. Explore here: http://www.makinghomeaffordable.gov/get-assistance/explore-eligibility/Pages/eligibility.aspx

If the first loan was originally a Federal Housing Administration loan or VA loan (not likely in a first/second scenario, but possible), you may have the ability to refinance the current first loan balance (with restrictions), petitioning the second lender to “stay put” with a subordination agreement. Beyond these specific scenarios, your options are likely limited. Double check with a local lender to be certain there are no local relief programs that may benefit you.