You could give Checkfront a try. It's not open source, but affordable and easy to use.
I am looking to implement an online booking system for a Personal Training business to take both payments and have a diary of dates available etc, having never worked with this kind of system I was hoping someone could point me in the right direction. Most of the booking systems I am finding are for Hotels or similar, I am preferably looking for one specific to the business and an open source system would be handy if one is available to keep costs down!?