Yes.
An Aussie bloke has developed an arrangement using two cantilevered struts that allows you to release a catch, and then when reversing the trailer is pushed the way you want to go, just reverse into the spot as if the trailer is not there and it will track exactly where the car is going.
No I have no idea if it is commercially available, it was aimed at the retired caravanner and was going to cost thousands to fit.
It was very good though - the trailer goes exactly where the car goes.
Cheapest effective solution? Fit a tow-ball to the front of your vehicle and push the trailer into it's parking spot, simple, easy. cheap. (I like the last bit best!) Using a car? There is always a strong nudge bar available that will handle a low speed job like this, if you can't fit one then your car is probably not suited to towing much either.
I am the son of a Truckie so reversing trailers for me is so simple it irritates the heck out of people. Dad showed me how to reverse the semi when I was 11 - we used blocks on the pedals, and my feet. When commercially fishing I will have the ute flat out in reverse for a hundred metres around corners and want more speed, I hate watching some old(er) codger take five minutes to go four feet and still not straighten up while I am waiting at the ramp with a load of fish in the sun!! (I know - impatient bugger, but I do it for a living, so...)
Having said that I have a dyslexic mate who jack-knifes into every spot - nothing helps there other than him taking his time, and resetting time and again. He hates launching boats or going to the dump so we do it for him. Given space and privacy he's o.k. - but put under pressure he is stuffed every time.