I appreciate this is a really old post, but having just experienced the same problem myself this afternoon (despite never having had a problem in the past with around 50 previous projects!) I thought I would post the solution I got to work.
Despite saving the image I wanted to use as a .png file with a transparent background, as soon as I imported it into iMovie and clicked the fill option (so that all of the image would appear), the black background reappeared. Doing a little research on the Internet, I discovered this was unavoidable because of how iMovie interprets the 'fit' and 'crop' commands, despite having a play with some of the settings within the 'Project Properties' window. I also tried re-sizing the water mark as suggested by someone on YouTube to match the 'picture in picture' box within iMovie, which is 175 x 85px but still no good! The image was also really poor quality, despite saving it using hi-res settings.
After tearing my hair out for the best part of 2.5 hours, I finally found a solution! The video I was working on had been recorded in HD and I work on a 16:9 wide screen (Mac book Pro 17" with retina display). The only way I could get my .png water marks to display correctly (without the black background) was to start with a blank canvas (using PS CS3) with the same dimensions (I used 1920 x 1080 and not 1440 x 990). Upon saving each file as a 24 bit .png and dropping it into iMovie using the 'picture in picture' option, they displayed correctly. If the image was too small because of it being placed on such a large background, I simply added the image, then cropped the background to suit.
I've never had to mess around with water marks like this before, but it seemed to do the trick???
