Encouraging more players to join the rotation of goalkeeper boils down to support. Athletes respond and react to non - verbal and verbal feedback.  It is equally important to not only to be encouraging but also reflect that in your body language.  Coaches, parents, and players alike have to participate in positive feedback not just offer criticism.  More players will want to volunteer in goal if they felt like they would have fun and succeed.  On top of speaking with parents about positive feedback coaches have to teach the art of goalkeeping in a fun and challenging environment.
In my experience as a team and goalkeeper coach, I have noticed the parents of goalkeepers tend to move away from other parents and are less vocal compared to the parents of field players.  Goalkeeper parents tend to be observers of their keepers performance as well as other parents’ reactions.  This is due to a few factors: nervousness for the their keeper and other parents criticism.  Parents are brutal a times forgetting that no professional athlete is perfect let alone a youth soccer player.  The goalkeeper needs to see all parents including their own cheering for every player and action; applauding not only for the diving save but every punt, kick, and catch.  Find something good to cheer about.  Reassurance will help build confidence in your developing keeper and athlete.  During games display a calm demeanor, refrain from derogatory and critical remarks towards players and officials, and applaud the simplest of accomplishments. 
As parents and coaches we have to teach our young athletes about sportsmanship and fun competition. During every opportunity we must reinforce that this is a game and it is fun.  If the game of soccer is seen as a learning opportunity and a chance to enjoy fun competition with their friends the whole atmosphere will be more relaxed.  I remember being so nervous in goal when I first started playing. I was worried about making a mistake or letting my team down constantly.  Having to worry about making a mistake consumes a player inevitably allowing a mistake to occur because of nerves and self - imposed pressure.
There should be zero tolerance within your team and on your sidelines for derogatory comments.  Drive this home early to your players and parents.  Finding a way to help your players and potential keepers experience success during practice will also help build confidence in games.  If more players see the goal as a fun challenging opportunity more will want to take a turn.
Giving your parents a list of positive statements and different ways to say “good job” to the keeper and all players is way to promote an encouraging environment.  The positive statements are endless:  nice save, good deflection, wow what a punt.  If the keeper comes out of net to challenge a player, “ way to challenge the shooter”. If a goal is scored:  “ You were close, You’ll get a hand on it next time, It was a good shot, not your fault, pick you head up and you’ll get the next one”.  After the game have you team find the keeper and congratulate them first.
Help take the pressure off the player in net with your words and actions.  Celebrate the players are having fun and learning.  Set a good example for your players and parents by being positive and encouraging.  Positive feedback will build confidence in your keeper to make decisions, which will aide in their learning process. 

From a team development standpoint youth coaches should dedicate at least one practice to goalkeeping.  Teach every player at U8 to catch, the ready position, and distribution.  This will help identify potential goalkeepers to rotate in and out.  A majority of the players will love this fun session since most young athletes enjoy diving all over the place and being dramatic with the game winning save.  Having balls kicked and thrown at the keepers will help players develop a sense what it feels like physically and emotionally protecting the goal, being the last defender, or first attacker.  Having a foundation or the basic skills to succeed will help build confidence.  A swimming instructor would not throw a student in the deep end if he didn't know how to swim.?

Parents and Coaches alike should reward their player for being brave and protecting the goal.  Reassure the keeper that mistakes are learning opportunities.  The best professional keepers make mistakes.  Even watch a keeper bloopers DVD with the team as well as great saves.  Simply help them understand there will be shots that can not be saved since the goal is really big compared to the keeper and there are a lot of people trying to score.
Christian Benjamin, owner of keeperstop.com.  USSF and NSCAA licenses coach specializing in goalkeeper education.  Goalkeeper coach and clinician for college, ODP, high school, premiere travel, and recreational keepers and coaches.