There are only really 2 sizes for 10" wheels:
145/80x10 (standard skinny tyre suitable for rims up to about 4.5" width but trying to get any quality brands will be almost impossible barring Dunlop Aquajets mentioned below) or
165/70x10 which will fit on rims from 4.5" to about 6" width and are available in Falken FK07 (last quite a long time, grip pretty good), Yokohama A008 (very good grip, doesn't last as long as Falkens) or Yokohama A032R (semi-slick but road legal - sticks like poo to the proverbial blanket but doesn't last long!).
There are also Dunlop Aquajets available in each size from
Vintage Tyres which have the classic tread pattern. They are expensive and I've not had personal experience with the 're-make' ones which are currently available so can't comment on grip levels or mileage, but I get the impression they tend to be used mostly on show cars where the look of the tyre is the over-riding factor.
Hope this helps,
JR