Is 弄 + complement of result only used for actions with a negative outcome? MDBG translates 弄 as "to do / to manage / to handle / to play with / to fool with / to mess with / to fix / to toy with". When I look at example sentences with 弄 and a complement of result, I find only descriptions of actions that are somehow negative:


  
  他把我的电脑弄坏了。 (Yale University Center for Language Study)
  小狗把房间弄得很乱。
  请不要把顺序弄乱了。
  我不小心把衣服弄脏了。(Last three examples from Mandarin Chinese School: New HSK Level 4 Vocabulary (Chinese-English))
  


Can 弄 only have a negative complement? Or is this just the most common usage? (If positive outcomes after 弄 are possible, please provide an example.) 
Note that I am interested in 普通话 rather than local dialects.
No，it can be followed by positive outcomes.
In your examples, they are followed by adjectives such as 乱、坏、脏, which are correct.
However, you can also say

我的电脑坏了，是李明帮我弄好的。My computer was broken, Ming Li fixed it for me.
你能帮我弄一下吗？Can you help me to do/fix this?
他把这个弄得很漂亮、很整齐。He made it very pretty and tidy.

In conclusion, 弄 can be followed by both positive or negative outcomes.