I don't know if it will fit for a contest, but how about online only cards? like a card that takes a card from your deck without looking at it or a card with limited number of uses for example
This is a potentially interesting idea. Every 6-8 months or so I forget why I stopped playing Hearthstone the last time and go back to it for a day or two, and I'm always a little surprised when one of my cards changes in my hand or my deck; and not just the cost, but the cards' strength/abilities can change. That game has other mechanics that are seemingly impossible to do with physical cards.
Some of those mechanics like "discover" (which gives you three choices from a larger pool of potential cards, and "creates" a copy of the one you choose) actually have pretty effective equivalents the game (see Black Market). Similarly, the pile Tokens from Adventures has the effect of making cards in your deck/hand stronger.
For the first one, it doesn't seem to me like there's any reason that could only be online. You could have something like "Shuffle your deck, then take the top card ..." There's already precedent for cards that cause you to shuffle your deck without the discard pile
I was thinking in something like draw an action from your deck, or some specific card like silver.
While "draw your next Action card" could be simulated with a mechanic like the ones in Venture/Golem (digging through your deck until you find one), there could a couple of reasons you wouldn't want to do it that way: (1) if you had a strong reason not to be churning through the deck (I'm not sure what it is, but it is at least possible), and (2) if you didn't want to know what the Action card was. You could imagine a card that pulled the top 3 Treasures from your deck, and set them aside to give you next turn. Not knowing what they were could be a way to balance such a card (since it would prevent you from knowing what you got, and whether, for example, you should play a Bridge Troll to maximize the following turn). However, I'm not sure either of those are going to be compelling enough reasons to make a card online only.
I see two clear ways online only would be substantially justified. Freddy10 mentioned one of them:
or a card with limited number of uses for example
As mxdata said, a card that has more than one and fewer than unlimited uses (e.g. something between a Horse and a Lab) would be extremely easy to do with an online-only card, and fairly onerous (though not technically impossible) IRL.
The other obvious reason to make a card online only is to avoid the problems that can arise around issues accountability. This is discussed in
Item 15 of the "Fan Card Creation Guide" and makes, for example, a card that you would be required to play if it were in your hand not feasible, because there is no way for other players to hold you accountable if you don't. Online, the server knows all, and can force you to follow a card's rules without the other players knowing.
Similarly, you could have cards that, for example, change their position in your deck without anyone knowing exactly where they are, or which replace themselves while in your deck with a random card without you knowing. You could have a junker which puts a random $2 or $3 Action card on top of your opponent's deck, which might screw them up or which might be a harmless (or even helpful) Pawn/Villager.