You need:
Number of the picture tube from it's label.
Resistance readings of the vertical and horizontal yoke windings. Here's how to do it:
http://www.8liners.com/datatech/monitor.html
If the yoke resistance specs of your existing tube are close enough to what the Wei-ya chassis calls for, then you use the existing yoke on your tube. You don't have to touch the yoke or the rings.
Alva Amusement, 8liners.com and Billabs all sell Wei-ya replacement chassis. Alva has the best selection and prices. The prices are no longer shown on their website so you have to telephone them for a quote.
http://alvaamusement.com/
http://www.billabs.com/
http://www.genao.com/osc/catalog/index.php?cPath=22&osCsid=6803fd3ac597503e71e88fcda4e675c7
Once we know your basic tube and yoke specs we can suggest the appropriate Wei-ya model to order. Also, does your Zenith monitor use an isolation transformer in the cabinet? I think it does, but will need you to confirm it.
Then once your chassis arrives, you'll need to "Americanize" it:
http://forum.arcadecontrols.com/index.php?topic=97584.0