If your buyer has a home to sell before they can buy your home, I have some recommendations for you to consider. I suppose my first and foremost would be DON'T. But if you do,.....First, never give more than 30 days for them to get their home under contract. You can always give them an extension, and many times as consideration for your giving the extension, your buyer agrees to reduce the price of the home they have to sell.
Of course I believe your buyer's home should be listed with a Realtor, so you can be assured they are on the market at the right price and are making their best efforts to get the home sold. If it's listed with a Realtor, call that person and get some feedback. Remember, while your home is under a contingent contract, you cannot accept another "contingent" buyer who may already have their home sold and is just waiting for it to close.
And, if a non-contingent buyer for your home appears, you need to make sure there is a clause in your agreement with the contingent buyer that their offer can be "bumped" with 48 hour notice if they cannot remove their contingency. That leaves it open for you to accept a non-contingent offer subject to canceling out the first offer. Be careful to word this correctly so you don't inadvertently end up agreeing to sell your home to two different parties at the same time. It's happened before, and that's a serious problem you don't want.