First, let's get straight what tires you actually need. You can't trust what's on the bike because some shops will do anything to sell a tire and some owners will do anything to avoid spending money.
Perusing the fiches, I come up with the following:
3.25H19 front
3.75H-18 rear
OEM was Bridgestone or Dunlop, and they used tubes. BTW, you can use tubeless tires on tubed wheels no problem -- just install a tube.
I'll avoid the whole "should I convert to tubeless" holy war for now.
Converted to the nearest modern tire size equivalents, you get:
100/90-19 front
110/90-18 rear
Both these are a little big, actually -- the conversions end up sort of in the middle -- so 90/90-19 and 100/90-18 are also legit.
Now, discard any outdated low-tech Chevy Impala based tire thinking. On motorcycles, wider is NOT always better. Stuffing on phat meats stuffs up the handling as well. What once was nimble and stable becomes slow, heavy, and unpredictable.
Now toodle over to American Moto Tire (my fave source for weird rubber) and see what's available. There's not much they don't have.
The front is easy -- there are zillions of 100/90-19 tires out there and lots of 90/90-19 as well.
For the rear, you have the following available in rear 110/90-18 (careful -- lots are front-only)
Do NOT install these Kendas. You will die horribly. Yes, I know they're cheap. They're also crap.
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=2513
Conti Classic -- innnteresting. But not at all vintage-looking if you're the sort of weirdo who prefers to look at tires instead of riding on them.
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=6383
Shinko 712. Very nice budget option. Looks modern:
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=5129
Duro. Still too zoomy looking...
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=5411
IRC Durotour. Good tire, looks close to vintage, and IRC made a lot of OEM tires for Japanese bikes:
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=2169
Pirelli Sport Demon. Very sticky. Short-lived. Looks all zoomy and stuff.
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=4040
Bridgestone S11. Bleagh.
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=744
Avon RoadRider. Looks modern, but probably about the best vintage tire available. Great feel, stick, and wear:
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=461
Bridgestone BT45. Great modern tire, more complex look you might like better? Dunno.
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=696
Conti Go. Another great modern tire. Looks modern:
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=4882
Dunlop 404. Very traditional tread pattern. Not that great a tire. Short-lived and turns evil as it wears.
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=728&products_id=4882
I couldn't find any 3.75-18 tires, but if you're willing to bump up a skosh, there are some very vintage-looking skins available in 4.00-18. For example, the IRC GS-11 is the exact same tire supplied as OEM on many Japanese bikes. Exact same 1980's performance, too...
http://www.americanmototire.com/catalog/product_info.php?manufacturers_id=714&products_id=2152
Personally, I think it's beyond silly to worry about a tire having the right vintage look. If you're going to ride the stupid thing at all, take advantage of the excellent modern rubber now available. Once it's in motion, no one can see your todius old-skool tredz anyway.