Well Larry - in general the carb you need is a Carter #26 as David noted above. The #26 is the size of the Venturi opening, and if you have a look inside the carb from the choke plate side, you should see the numbers "26" stamped on the inside top. Unfortunately that isn't enough info for you to find a correct replacement carb.
So, the first thing I did was pull out my handy dandy Kohler K-series Service Manual and looked up the Serial number for the engine you identified. Sure enough 9715118 shows as a Kohler engine built in 1979. But since you said your tractor was from 1980 the next thing I did was pull up the IH Cub Cadet build date chart. According to the chart your 1250 with serial number 658199 was actually built towards the end of the month of June, 1979. That matches up to the Kohler engine build year. Then with my thinking cap on, I can pretty safely say your Model 1250 has its original Kohler K-series Model K301AQS engine (unless someone was screwing around with it).
So, with that information in hand, the next thing I did was go to the Forum main page thread and
selected "IH Cub Cadet Tractor Forum",
and then I looked down the list and selected "Link to CubCadet Parts",
and then I clicked on the link titled "Lookup Parts via Diagram l Cub Cadet US"
which takes you to the Cub Cadet Corporation website link
and then I clicked on the gray box that says "Cub Cadet",
and then I clicked on the box that says "Garden Tractor",
and then I scrolled down the list to "1250 2050059 2050610U 2050630" (the latter being your tractor)
and clicked on that link, which takes you to the top right side of the page and I selected the 2nd box shown as
"Assemblies for 1250 2050059 2050610U 2050630" and clicked on it,
and scrolled down to the box titled "Engine-K301aqs-12 Horsepower" (which confirms "your" engine model number)
From here I could see a diagram of the engine, and after enlarging it I could see the carb was diagram item #42.
I looked up item #42 on the right hand list and it shows Part No. KH-47-853-20 as the carb assembly for your engine.
So, with Part No. KH-47-853-20 in hand I went back to the Main Forum page and clicked on the colorful box at the top of the page for CC Specialties. That took me to Charlie's web site CC Specialties where I inserted the part number in the search box. Up popped 2 links. The first one took me to a page of Carburetors and I scrolled down to find your part number.
I found it in the following box.
| Aftermarket Kohler Carb Replaces PN/ IH-385472-R91, KH-47-853-20, KH-47-853-22 or KH 47-853-22-S
Fits 10 and 12 H.P. and 14 H.P. K241 and K301 #26 Carb
Fits 70, 100, 102, 104, 105, 106, 107, 108, 109, 122, 123, 124, 125, 126, 127, 128, 129
1000, 1200, 1210, 1250, 1450, M10, M12
Click the small pic to check your linkages are close or the same! | $70.00
|
(here's the link that will take you to the page with this box):
Cub Cadet Kohler Carburetor Parts International Harvester IH IH-385472-R91 USE KH 47-853-22 KH 47-853-22-S IH-385389-R91, KH-41-853-11 USE KH-41-053-13 CubCadet MTD CCC carb Parts
In Charlie's description it says to click on the small pic to check your linkages are close or the same. I did that looking for that dog-leg type choke lever which I believe all the K-series AQS engines in Cub Cadets used (based on my memory). It sure looks like this aftermarket carb that Charlie has, would be the correct carb for your 1250. BUT, I don't know for certain if the linkages in the picture are correct. The only thing I recall is that dog-leg choke lever.
The next thing I did was go back to the other link for a carb in Charlie's listing. It took me to an OEM Kohler carb but it's NLA.
So, it looks like you can get a brand new carb for your 1250 for $70 from Charlie (plus shipping). I have to say to me that's quite a deal.
On the other hand, I don't really know why you want to replace your original carb. I've always had good luck overhauling or rebuilding them and Charlie has the kits on his Fuel Tune-up and Maintenance page. The overhaul kit is pretty cheap (just the needle, seat, float hinge pin and a couple gaskets). If you need a rebuild with a throttle shaft bushing or even a throttle shaft that's more expensive now, involves more work, and based on the parts cost it's cheaper to just get the aftermarket carb.
Hope this info helps you,
(And helps others on the Forum figure out all the steps to get thru the links to find the CCC parts look-up).