Here are three practical suggestions for making suggestions that work:
1) Only make suggestions when you have a connection. There's no point in making suggestions to someone who is not listening. The best advice is advice that gets heard - so get a connection before making a suggestion.
2) Suggest what you want - not what you fear. We all know that it's hard to hear all of a suggestion. The easiest part to miss is the negation - hypnotists say that "Do not think of red apples" and "think of red apples" are roughly the same suggestion. So let go of fear and irony and suggest exactly what you want.
3) Make the suggestion more than once in more than one way. If you're not committed enough to think of different ways to suggest something, why would someone else be committed enough to follow the suggestion? Mindful repetition makes an impression.
Think about something you'd like to suggest. Get a connection. State what you want simply and clearly. Then find three more ways to work it into your conversation (ensuring you have a connection each time).
Try it. Connect, suggest, repeat.
Like I just did.