For 1 cup, use
1 cup honey; OR 3/4 cup firmly packed brown sugar; OR 1 cup dark corn syrup; OR 1 cup pure maple syrup.
The suggestions by CarlaJS sound good, but your results will depend upon the recipe. Molasses has a pretty distinctive flavor so if the dish you are cooking depends a lot on that flavor you will notice quite a difference. On the other hand if it is mainly used as a sweetener such a substitution might be less noticed. Also, you might find you like the dish better with a different sweetener, so I'd say "go for it!"... that's how to find new or different dishes. If something sounds to you like it will work, give it a shot (on a small scale) and see how it turns out.
My kitchen is my playground... and my laboratory. It is a great learning resource for me provided I adhere to a few simple rules:
1: Never be afraid to experiment; if it sounds doable, it probably is.
2: Always experiment in small batches. This keeps costs manageable and makes rule #3 a lot easier to swallow....
3: Always eat your mistakes, as well as your triumphs. This reenforces the learning experience. It also helps keep costs down, and if you create as many disasters as I have it will keep your weight down too! And....
4: I'm still bad to neglect this but it is perhaps the most vital rule (except maybe #1): *Keep Detailed Notes!* Write down ingredients, quantities, temperatures, utensels used, whether your cat was in the kitchen.... anything that might affect the outcome of the dish. Leave extra space in your notes for sub-notes... ideas, improvements, improvisations that turned out to be very (or moderately) bad (or good) ideas, and details on those.
This last is very important as we get older (and as you will see if you haven't already), because while our innate confidence in our ability to remember tends to remain strong, our actual *memories* are usually the second thing to go. Keeping good notes, writing things down, becomes more important the older we get, but even if you are still young it's a great habit to get into. Heck, if I'd been keeping good notes a few decades ago I'd probably remember what the *first* thing to go was... if not I could look it up in my 'notes'!
If you're after the taste of Molasses, nothing can substitute for the sulfur that makes it tasty, believe it or not. However, the brown sugar/syrup will be the closest flavor. God bless you. : )