Depending on how your deal is, meaning its going to be a contract for a fixed amount or just hour based, the size of the game etc.
If I were you I would just write up all the features that client want, like:
2 player support
Have to make sound
Have to make graphic (animations or stills, Quality etc.)
and so on.
And then estimate how long you would have to spend on each part, and based on that and how much you would prefer to be paid for a hour of work, you will get some estimate of the final price. If you do this privately you have to take into account, all the benefits that you would normally get from working at a company that you don't get, if you work as freelance. The "normal" benefits will of course differ from country to country. But will give you a higher price per hour.
If your idea is to primarily use the game to promote yourself, rather than making money on it, you can of course just lower the cost, so the client is more likely to accept it etc, and in the end you can use it to maybe get more customers.
Anyway that's roughly how I do it, when doing freelance work, and it works fine for me as you wont suddenly feel that you are working for free, or that you are screwing the customer. But if you work on a fixed contract, you might end up having estimated wrong, regarding some of the things, forgotten some and so on. So I would suggest really spending a good amount of time, making sure that you have gotten all the features down and made part of you estimation, and ofc make it a lot more detailed than my example above