There isn't any easy way to do that.
But you should think carefully about why you think that "using a VPN only in a specific browser" will do for you. I suggest that you read
Tunnelblick's Privacy and Security page for information about using a VPN. It might help you clarify what you are trying to do.
I think you could achieve the same effect by using a proxy, because most browsers allow you to set up a proxy specifically for that browser without affecting the rest of your system. That proxy could then use a VPN, I suppose, but depending on what you are trying to accomplish, you might want to have the proxy use a VPN.
I can't help with using or setting up a proxy.