You can always meet c5 with d5 which leads to Benoni kind of structures. But you have other options, too. Here's what I play. Not necessarily the most challenging way but at least I get positions I'm comfortable with.
What to play against the old benoni?

The old Benoni is easy to get an advantage against, but you cannot use the London or Tromp against it.
1.d4 Nf6 2.Bf4 c5 is NOT the old Benoni. That's a straight up line against the London System.
The old Benoni, 1.d4 c5, is rarely played because most Benoni players now wait for c4 to be played by White, taking that square away from the Knight.
Against the Old Benoni, 1.d4 c5, the solution is 2.d5! (The ONLY good move here) Nf6 (or 2...d6) 3.Nc3! (DO NOT play c4 here) with ideas of playing e4, Nf3, Be2, O-O, and the Knight from f3 to d2 to c4 and later Bf4, putting pressure on d6!
that's what i know about those two positions. you can easily find the youtube videos for the 3 e3 line. i think the line with the pawn sac on b2 you actually get from a tromp move order so if you are well-versed you should know of it.
anyway i don't play the tromp or the london anymore so someone else could point out some subtleties here or mistakes even.

Old McLaughlin has a farm of ideas what to do against the Old Benoni:
(I saw the video, if Black plays regularly, he's too short on space)
https://www.youtube.com/watch?v=cUBKWSiQF-s

If you like gambits:
Now you're in the Smith-Morra gambit :-). But since you're a 1.d4 player... it may confuse You more than your opponent...
It's more likely that a benoni player also plays the sicilian than a 1 d4 player also playing an open type of game with the morra or even just the open Sicilian after 2..cd 3 nf3!? You normally choose 1 d4 to avoid early tactical fights.

You could try the Liedmann Gambit as shown above although higher rated opponents will avoid this and play d4 c5 c4 d5 and now you're in a QGD : Austrian Variation !

You can just play the old benoni... there's a reason it's called 'old', just like "Dragon", "Acc. Dragon", "Hyperacc. Dragon", what does that tell you? ...
You could try the Liedmann Gambit as shown above although higher rated opponents will avoid this and play d4 c5 c4 d5 and now you're in a QGD : Austrian Variation !
What do you mean? by "higher rated opponents will avoid this d4 c5 c4 d5 and now you're in QGD : Austrian Variation"? What moves will you and these higher rated opponents do? I genuinelly want to know because QGD: Austrian Variations generally turn out good.
I play the London system and the Trompowsky with white, but I don't know how to play after 1.d4 c5 or after 1.d4 Nf6 2.Bf4 c5. Can you help me?