Ok, so let's see if we can understand what you're trying to do.
1) You've found 1.25" balls.
2) You want to use this ball to hook up a garden trailer to a tractor.
You asked for a receiver, but what I think you're looking for is a coupler. Otherwise, there's no relation between a 1.25" ball and a 1.25" receiver.
So, if I understood what it is you're trying to do, my suggestion is to start with an anti-sway kit. (Here's one at CW
) Install the ball into the hole on the back of the lawn tractor where you typically would drop the pin for the garden tractor. Then, pull the center out of the anti-sway, which provides you with a coupler already welded to a straight stock of metal. This will need to get welded to the tongue of the trailer, effectively making a new coupler.
Then, when you go to hookup, just drop this coupler on the ball, insert the pin like you would when using it for anti-sway, and away you go.
Note though, that this is just an exercise in whether or not this could be done. For all practical purposes, this kind of connection shouldn't be any better than the existing pin in hole method the trailer/tractor uses currently. Both require a drop in place, insert pin, so all in all I'd stick with what's already there.