Why would you want to program for this thing for the first place?
I guess borland C/ Turbo C should prabably work on it.
There is apparently also a Turbo C++.
And here's another source for various such things.
But I have to say, if you're really going hardcore old school, you need to code in assembler.
YOu might be able to use Turbo C 2.01. I could when I had a Tandy 1000HX.
Oh my God, I haven't seen one of those in forever. Okay, that's running a version of MS/DOS, no later than about MS/DOS 3 as I recall.
First thing is to make sure you can read and write a floppy on the XP computer that the Tandy will read.
You'll need to look for a fairly old version of Turbo C, even, I'd guess. You probably should look into the Tiny C Compiler.
I would totally go for Turbo C that others have mentioned on here. They are very fast, easy to use, and in general have made me happy when coding in DOS.
PS: How do you plan to get Turbo C from the internet onto your machine? Via a terminal file transfer over serial port?
The Digital Mars C++ compiler claims to still support 16-bit DOS and Win16.
I'm not sure if the compiler itself will run on those platforms or if you'd have to 'cross compile" on a Win32 system and copy the results to the Tandy.
Actually, I'm not sure it works at all, but the support claim is pretty prominent.
The nice thing about going with Digital Mars is that you'd be able to use a much more modern compiler than the old Turbo C/C++ that's freely available. I imagine that template and STL support is much better in Digital Mars than in the old Borland compilers.
Though, the old Borland stuff might have better out of the box UI frameworks and such or old DOS source code that you dig up might actually work better with the old compiler.