Solving personal conflicts and giving constructive but personal feedback are two of the hardest parts of being an Agile Coach. I usually say that most problems are quite easy to solve once identified, but personal conflicts and issues between team members can be very difficult and require great creativity to solve.
Two great blog posts on this subject are:
Handling a team member who talks too much which uses the ladder of inference technique, and this post on creating the preconditions for constructive discussions
It is also extremely important to focus on the behaviour not on the individual. A persons actions are not who they are and you shouldn't assume to know the persons attitudes or reasons for the exhibited behaviour. Dominance, for example, usually turns out to be a sign of insecurity. You may find that building the persons confidence with positive feedback and encouragement (often counter-intuitive when dealing with a dominant person) will accomplish just the change in behaviour you are looking for.
Be concrete in your examples, cite specific instances but nothing more than 4-6 weeks in the past. Remind the participants of the situation and then state how this situation made YOU feel. Do not judge or criticise, merely explain how this behaviour affected you and what emotions you felt. Try to get the person to empathise with your feelings and situation and then ask them how they can help you to avoid this feeling in the future.
A talking stick is often useful when exploring an issue in a group as it allows people to talk through until they are finished without being interrupted. Always use an arbitrator - a neutral party - that can act as referee and make sure we stay constructive.
All coaches and managers should receive regular training in communication and conflict resolution. But the most important is that they maintain a neutral and non-judgemental attitude to all of the team members.