Hey mate. After searching around, from what I can see, you can't buy charging port replacements for the PSP Vita, only data ports. Even so, to replace it would require you to de solder the existing port and solder a new one on. Being basically a SMD component, it would be difficult to do. My advice is, see if there is a local console/gaming systems, repairer near you. They possible will be able to help you out with this.
Sorry its not much help.