Here are some tried and true methods:
Fess up: Try to keep in mind that being a conflict avoider is nothing to be ashamed of, that the majority of people have issues with conflict, even those who attempt to intimidate others with threats and aggression. They are just dealing with their fear differently than you are.
Practice self-forgiveness for all the times that you have judged or punished yourself in some way because you felt ashamed or weak.
Forgive others who you have harbored resentment towards or punished by direct or passive means.
Tell Yourself the Truth: Compile a list of people in your life starting with the most important relationships, whom you have failed to be truthful with or have withheld your feelings and in doing so have accumulated resentment that has contributed to a diminishing of trust and respect in your relationships and make a list of specific resentments that you have towards each person.
Feel It: Give yourself permission to feel the resentment, anger, outrage, or whatever other feelings that you have not permitted yourself to full experience and identify the fear that kept you from feeling them.
Take responsibility for your part in the creation of your conflict-phobia by your withholding your true feelings from yourself and others. Taking responsibility for your part does not relieve others of their responsibility it merely reminds you that both of you have played your parts in creating this system.
Invite your partner to join you in a conversation about “some things that I’ve been needing to talk to you for a while, but I’ve been putting it off”. Note: you need not use these words, but try to issue the invitation as a request rather than a demand or threat. The tone of your words is more important than the words themselves. Keep in mind that they are probably much more anxious or fearful of conflict than you may have believed him or her to be.
Take a respectful stand: If they want to know more about just exactly what it is that you want to talk about don’t go into any specifics but speak in general terms such as “I’ve been having some ideas about what some things that we could do that might help us to make our relationship even better than it is”. If your partner insists on more detail, this is your golden opportunity to and let him or her know that you prefer not to get into it now but to wait until you can both put aside more time to give this conversation the time that it deserves. If they insist on extracting more information from you, ask them to please respect your preference and see if you can come to a time agreement. If they persist in their efforts to break down your resistance, try to avoid getting angry or overheated and let them know that this just isn’t a good time to get started on it and ask them to please respect and accept you feelings.
Apologize: Let them know that you’ve recently realized that you have something to apologize for. That should get their attention. Go on to explain that you haven’t been completely honest with them about some of your feelings, concerns, and needs and that you want to come clean about.
Declare your intention to clean up the difficulties that your withholding has caused. Ask them if it’s OK with them for you to give them some examples. If they say yes, then try to express them without judgment of your partner. If they get defensive or try to correct you or justify themselves, politely request that they give you a chance to finish with the example that you’re offering and then you’ll be happy to hear their response.
Thank your partner: When the time comes for you to have “the talk”, thank your partner for joining you in your efforts to enhance the quality of your relationship
Admittedly, this is a process that will require more conversations regardless of how well the first one goes or doesn’t go. But with gently and committed persistence defensive patterns, even those that have been in place for years or even decades can be eroded and replaced with interactive patterns that can transform the most deadlocked stalemate.