I found a 1 inch strainer at the Meijer Dept. Store in my town.
Cost $.99 cents.
It is a Plumb Craft SF-9 strainer. Also has a number on the package 7638412-P. The SKU 0 28905 76384 4The card shows WWW.waxmancpg.com
Fits our 1 inch basin drain perfect.
Also saw some of these 1 inch strainers on EBay and Amazon, but for $3.00 or $4.00 dollars. EBay and Amazon also have various other basin strainer sizes for drains larger that 1 inch.