First on my list is teaching experience in a number of different environments. This might be different schools, different grade levels, different ability levels, different subject areas, and a few more.
I would add to that list that there needs to be a significant number of years in the teaching profession but, time alone, is not an automatic qualifier (or dis- qualifier). Some people are just darn good at connecting with other adults and the ability to connect trumps years of service.
Next on my list is the ability to be receptive to change. I am reminded of those teachers I was working with in the early 90's who couldn't see how computers would be used in the classroom. I not only had my own computer (since 1985) but I was mad that I couldn't afford the latest Apple IIe when I started teaching in 1992. Good coaches must be able to recognize the latest "thing" that is coming to the world of education and must be ready to use their imagination as to how this can be used in the classroom.
In today's world that would mean the use of technology and the use of social media. Good coaches should be listening to what educators are saying about how they are using technologies in their classrooms. They should be knowledgeable in how 1:1 programs are being implemented. They should be actively trying the latest apps and software so they are able to ask questions and make recommendations. And, they should understand that social media means more than just Facebook and Twitter.
I would be remiss if I didn't comment on the use of Twitter though, since I find it so valuable in my own teaching world. Coaches these days should be active on chats such as #educoach and #edchat or #ntchat (new teacher chat). If they are an elementary coach they should be involved in one of the many chats geared at those grade levels or just #elemchat. If they are high school then they are probably course specific and they should be following chats such as #mathchat or #finedchat. And if they are something like a PBL coach then there's #pblchat.
These chats will give answers to questions at all levels of teacher ability and will allow coaches a chance to ask others how they might handle a question that has been posed to them. Then there are the hundreds of educators who are on at every hour of the day who might be able to answer questions on any range of topics. Finally, with twitter, there are many teachers using twitter in the classroom and coaches need to understand how this is being done in these other schools.
Education coaches need to be pros. As THE professional/expert in a certain area coaches must be willing to find answers and that means reading blog posts by knowledgeable educators and it means paying attention to sites like Edutopia, Discovery Education, The Buck Institute and even the Huffington Post (with an open mind). They need to be aware of trends and fads and should be listening to what students are doing and saying about their education.
The bottom line is that coaches need to be multi-dimensional. They need to be willing to work long hours when needed and they need to know when to say "I'm off the clock." They must be receptive to change while recognizing those things that are tried and true (and are still VERY relevant.) They need to know when to give a hug and when to (metaphorically) slap someone in the face.
I'll never know why I didn't get the coaching position I applied for but now I know that I need to become even better at all of these things I just listed. And when I do I will become an even more valuable member of my school and my students will be the benefactors of my hard work.