I am pretty sure that it will take 5w30. This information is located in the owners manual. As long as it doesn't get too cold in the winter in you area, then 10w30 will be fine as well.
The 2003 Dodge Durango has single overhead cam (SOHC).
5w30
5w30 or 5w20, depends on what is printed on the oil filler cap.
The 2001 Dodge Durango has single overhead cam (SOHC).
The 2007 Dodge Durango has single overhead cam (SOHC).
The 2011 Dodge Durango has double overhead cam (DOHC).
The 2009 Dodge Durango has single overhead cam (SOHC).
The 2004 Dodge Durango has single overhead cam (SOHC).
The 2012 Dodge Durango has double overhead cam (DOHC).
The 2013 Dodge Durango has double overhead cam (DOHC).
The 2006 Dodge Durango has single overhead cam (SOHC).
The 2008 Dodge Durango has single overhead cam (SOHC).