I'm late to this particular party, but here's an approach that's worked for us helped a friend in reputation management crises:
First, you need to get some indexed content for the phrase you're going to insert into suggest. I'll go with "Gibble Gibbet".
- Add a page to your own site;
- Or even better, find a phrase for which you already have indexed content.
- Either way, get some Twitter/other social traffic going to ensure it stays indexed.
Now, you need to get some search volume:
- Don't think of this in terms of directly generating search volume. Instead, think of this as a social engineering experiment.
- Determine what phrase you want to show up in search suggest. I'm sticking with "Gibble Gibbet".
- Create a test on a service like Amazon Mechanical Turk. Tell everyone involved you need them to tell you the first 2 results they see when they type in "Gibble Gibbet".
- Send out the test to 5,000 or more people.
Depending on the term, the search volume around it, and the competition among different queries, this should get you what you're looking for.
Not that I've ever done this.
It was a friend of mine.