I buy ball bowlers from 1957 to 1970 ball bowlers (bowling alleys) by United, Williams and Chicago Coin Machines (Chicago Dynamics Industries, aka CDI).
These are more difficult to ship, but often it is possible (please contact me if you have one for sale, and where the game is located - I am near Detroit, Michigan.) How to find a game easily in this document: This document is organized alphabetically by game type.
Sam Stern, president of Seeburg's Williams subsidiary, ran the United operation and retain his duties with Williams.
As late as the 1983, Williams was still using the United name on their Shuffle alleys (1983's Triple Strike was the last shuffle with the "United" name).
Unfortunately, in 1999 Williams stopped making all amusement devices (they only make slot machines now, under the Williams name).
The first shuffle alley, United's "Shuffle-Alley", in October 1949.
(taken from a October 1949 Empire Coin Machine advertisement).