The client asks to use an unfamiliar technology, what to do?

Discuss with the client the fact that this technology is not familiar to you personally. And there are already options. If the client needs to hold at any price, can offer him to realize analog on the basis of the technology, which is owned at the moment. If the client is interested in your services — to learn technology fast enough.
The costs of learning to invest correctly, because you are the expert and that is why the customer called you. Technology study for yourself, leave the amount unchanged, but the timing of the project are expanding commensurate with the complexity of the technology.

I have studied for yourself, then you and others offer, and take the loot for something that is unknown — I do not think that is correct.

To combine both, honestly explaining to the client the situation and lowering the price a bit with increased development time.
And it was interesting.
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Will also be fair to offer the client not insist on the new technology if a quick preliminary approach to the projectile revealed any comments.
For example, hardware requirements or the biggest looser among technologies in a noisy PR campaign around it.

It turns out that the client pays for your training — not only money and time you spend on learning new technologies and correction of mistakes, admitted inexperience (which, incidentally, will need to fix train all).
The sum upheld — and, in my opinion, goes a great way to resolve this situation.
In the end, this experience enhances your professional weight and ultimately the cost of your services. I believe this opportunity can only be glad.

To Google ;-) "Any whim for Your money", imho. If it is clear that technology is bad (obsolete[Ayu]shae uncomfortable), you can try to dissuade You if this is support then, but we need to offer an alternative where You do better, and briefly explained what was happening.

Most importantly just be honest. Then it will be easier. To say that technology you don't know, I would like to learn this technology, but unfortunately, the cost of your learning of this technology will be included in the total score. Or that you don't want to learn a new technology and the result accordingly is not predictable.

Steve McConnell well paced for such a situation. In short, you will convince to do the old, but stable. The rake will still come out.