Wingnut, some plastics can be welded and some just don't work too good, breaking down from even the lowest heat required to weld. I have had some amazing successes welding plastic and some dismal failures too.
I didn't get a clear idea of the shape of the damaged area but am assuming there is no missing material just a small crack or puncture. I have had success pulling a little vacuum on a plastic container and getting repair material to be sucked up through the crack. You don't have to reach inside with your hand or a tool. You can even enlarge the crack with a gently applied wedge or drilled hole(s) to permit sucking in thicker materials.
Sometimes it is good to drill a "crack stopper" hole at each end of a crack to reduce the stress concentrating effect of the sharp radius of curvature of the sharp "end" of the crack. These holes will be filled with repair material anyway and help the situtation not weaken it.
You can suck in enough repair material to cover the entire area around the leak (plus a little extra) then put, (dare I say it?), duct tape over the repair area on the outside, then while positioning the vessel such that the leak is the lowest point, relieve the vacuum and add enough pressure to force some of the repair material back out through the leak forming a slight buldge under the duct tape. If you use a two part (catalyzed) repair material just put down the tank with the patch at lowest point and wait for a good cure. If you use something like GE Silicone Seal leave the lid off the tank to admit atmospheric moisture (required for curring RTV-Silicone Seal that emits acedic acid (smells like vinegar) when curring. If you have real low relative humidity, wet a paper towl and place in the tank to provide a higher relative humidity (in this case you can put the lid on the tank).
The vacuum idea works pretty good but don't get too carried away and collapse the container. Brake bleeder vacuum pumps are one source of vacuum. A vacuum hose from a car intake manifold or carb is another. There are gizmos that are powered by a garden hose that are used to suck up water (venturi effect, see Bernoulli's principle) a flat piece of wood with a hole for a piece of tubing can be your temporary "lid" for doing the vacuum trick.
Best of luck to you,
Patrick