You must apply in your home country. Since 2014 the law changed and people can no longer apply for longer term visas in South Africa.
How long have you guys been together? Have you made sure you meet all the requirements for a life partner permit? Do you also plan on working in South Africa.
Read the visas for South Africa page for more information.
Most immigration consultants will tell if you are eligable to apply for a permit at no cost.