Google suggestions are based on what other people search for and, if there are not many pages found for the phrase you typed, for phrases with a much larger hit count in the search engine. This doesn't necessarily mean that your phrase is wrong, so don't rely on Google to correct your sentences in that way. It can, however, be useful to check how frequently a certain phrase is used by searching for two different phrases and comparing the amount of hits you get on Google.
Now, there is a difference between the sentences when using could or would:
The verb could expresses ability or possibility whereas would expresses a hypothetical situation. This is also why would is often accompanied by an if-clause in which you find that the condition for that hypothetical situation. The verb would could also be used to express a suggestion or advice, as in the phrase "If I were you, I would..."