If they're metal you may be able to weld a patch on the leaking area if you can get to it. There are serious risks that have to be mitigated, like emptying the tank completely and emptying and drying out the tank, protecting everything else around it, etc.
I've heard some people insert a rubber bladder into a leaking tank. It fills the tank to approximately the same size/capacity.
If it's a fiberglass tank I'm not sure if it can be repaired or not. I have no experience with that, but I imagine diesel saturated fiberglass might make it hard for new fiberglass to adhere and seal.
I would think plastic tanks would be easy enough to repair (though, again, I'm not speaking from experience). There are some effective glues, or you might be able to use heat.
Good luck, and let us know what you end up doing.