I want a Hitch for my Pioneer 500 so I can pull a14 foot boat and also to pull a garden cart around the Yard.

Just the 1 -1/4 Draw bar without ball from Honda is between 45 and 50 bucks so I am thinking that I would be better instead to get a 1 1/4 to 2 inch converter then I can put a 2 Inch drawbar I want on it and use a taller bar on it for towing the boat.

Which 1-1/4 to 2 inch Hitch adapter is inexpensive and would serve the purpose and how tall of a riser would you use to tow the Boat trailer ?

Stay with the class 2 ball mount. The adaptor will put unnecessary leverage against the Pioneer. Ball height depends on your trailer, remember the muffler is above the ball, leave room to decouple.

I'd use something like this. Short for leverage, long enough to keep it away from the gearbox if the trailer slips.
https://www.uhaul.com/MovingSupplie...r-2-5-8-Rise-Black-Powder-Coat/?id=11383

You can do a European style if you don't want an interchangeable ball. They look a little cleaner and the nut doesn't loosen.
https://www.amazon.com/gp/aw/d/B003B3EZFO/

1 1/4 ball mounts come in about any height you want. A quick web search will bring up lots of them and a lot cheaper than $40. Most that I've seen are in the $25 range.

I've used a European style to tow my kayak trailer for years and it's worked very well. Lighter and easier to stow than typical 2" stuff as well.

Does the Honda Pioneer 500 use a class 1 or a class 2 Hitch ?
If it is a class 1 Hitch then a class 2 Ball mount probably wont fit in it even if it is 1 1/4 inch from what I understand .

Good point, I don't remember, we might have cut down a class ii. A class i will do everything a Pioneer can.

Correct, a class i will fit in a classii but a class ii will not fit in a class i without cutting the shank shorter or drilling a new pin hole. The class i receiver has a block off plate to prevent the classii mount from inserting far enough to align the pin holes.