This question already has an answer here:
I tend to think of the Coppersmith card in Dominion: Intrigue as pretty much a dud of a card. Anybody have any useful tips as to how to play this card properly?
You are correct in your assessment that in most Kingdoms, Coppersmith is a poor card and you would be better off with something else or just Silver. It has a couple of problems, as you have seen. It's terminal, so it doesn't play well with basic drawing cards that could give you a hand full of Copper, like say Smithy. It doesn't provide a +Buy, so if you do manage to pull off some combo that lets you play it with a hand full of Copper, you'll need to add yet another piece to actually use your money. And assembling a powerful combo is difficult since you need to not trash your Copper or even discard it to, say, Warehouse.
That said, Coppersmith's best friend is probably Tactician. Tactician provides big hands with plenty of Copper, another Action to play with, and that critical +Buy that lets you actually do something with all of your money.
As Paul Marshall's answer hints at, a T1/T2 Coppersmith is fairly likely to connect with three Coppers and provide a T3/T4 Gold. That can help you get off to a good start, but then you have this increasingly-useless card in your deck. The presence of trash-for-benefit cards like Remodel, Apprentice, or Upgrade can make this kind of Coppersmith opening more attractive.
The Dominion Strategy Wiki has some more discussion. It also suggests that Coppersmith can be a boon to a very powerful draw engine that doesn't need to trash. Some combination of Wharf or Council Room (draw and +Buy) and King's Court or Throne Room (to magnify the power of the drawing) might make you take notice.
Coppersmith improves your early hands at the cost of your later hands.
Buy it with your opening hand(s); its only purpose is to accelerate your deck in your early turns. The next few times you see it, you'll probably have about 3 coppers in your hand, which means you can immediately afford Gold or other 6-coin cards. Compare it against a Silver: a Silver will give you +2 coins, but a Coppersmith will give you +3 or even +4 coins in those early hands. If you don't have any trashing cards, then you'll see its value degrade to +2 coins, then +1 coin, and soon enough you'll draw Coppersmith hands with no coppers at all. If you have trashing cards, then get rid of your Coppersmith as the number of coppers in your deck decreases.
There are worse things in Dominion than having a single card that won't be useful in the late game; your entire initial deck consists of such cards, so one more such card isn't the end of the world.
Finally, if you happen to play with both Prosperity and Intrigue, and the board has both Coppersmith and Counting House, and the Random Number God likes you, then you should fill your deck with Coppers and +Buy cards (with a few +Action cards to let you build the chain). Then you can play both Coppersmith and Counting House in the same turn, draw 15 doubled Coppers from your discard pile, and buy the whole world and everything in it. Do not count on this working out on any regular basis. It's great fun; if you play Dominion in order to create entertaining combos rather than to solve its statistics puzzle, then go for it.
There are certainly better cards out there. But if the other 2-to-4-coin cards in your current game aren't exciting, or you have a strategy that requires 6 coins before the other players, then Coppersmith will get you there faster than Silver will.
(Note: I have not played 2-player Dominion; my experience is exclusively multiplayer.)