Unlike colleagues, I would not be so pessimistic in assessing the situation. Yes, this is not a simple case. It's even slippery. I can imagine multiple scenarios depending on your company's culture of work.
I don't believe it can happen in a harsh environment with a very strict, hierarchical management style as no one can fit two different personalities in one person. But as well, I don't believe such management style could work for a long term agile software project. So let's assume you have rather soft relations and your team is driven mostly by intrinsic motivations.
- You will not have enough time for both roles. Each one is a demanding one and you will most likely sacrifice some quality factors or will be forced to delegate some tasks.
- You will need to check what hat are you wearing, need to check it frequently and also make sure it is clearly understood by people you are communicating with. Even if you manage to do it, it may be difficult for others to switch their thinking so often. And it is like being an AA, it never stops, it is never over.
- You will be empowered, so it will be easy to switch hats and danger is that you will want to use the manager's decisiveness to solve the problems of a coach. Bang! A Joker card!
- They will try to make you make decisions. From time to time there are problems to solve or difficult decisions to make by the team. You may be involved and think you gave just an advice to consider, but later you will hear "We talked, and YOU decided...". So, avoiding micro management and giving a (shared) responsibility is not simple task.
On the other hand there are also pros:
- Both roles can have a common goal - to help the team. Not every manager remembers about that and not every manager is so much aware of the problems as Scrum Master is.
- You will be empowered and it is rather a good thing if used wisely. As Zsolt said: ...you can get budget for improvements, protect the team from external issues, escalate issues sooner and more effectively ...
- The close relationship. I don't agree it won't work. You can set goals to achieve, give some harsh feedback, make unpopular decisions and maintain the relationship. But some managers go for short-cuts and they forget about honesty, openness and trust. Maybe it is easier to lie, feel omnipotent and make empty declarations but don't blame the relationship. It gives you a chance to know people's true motivations, receive their feedback and have a healthier atmosphere.
Well, about the advices...
As a coach ask questions, clarify the rules and give examples. I would avoid sentences like I recomend..., I would like having it that way etc. Avoid stating your will, instead ask the questions and give examples: Let's consider the possible solutions..., What would be better...?, What are the pros and cons...?
Let them think, a coach makes people think.
Be a manager when you supposed to. Manager is an observer on a daily stand-up meeting and on a retrospective. Scrum Master is supposed to talk, let the other hat be silent.
But then, management is supposed to remove the obstacles, give someone a feedback, shield the teams from the outside (and do many many more). You can not end your work where SM would.