Big sheet of cardboard with a design painted upon it. Have a few holes in it for "prizes".
In painting the design, perhaps you can think of biblical references. Good samatian, Judas's 30 pieces of silver (make it to the object is to *not* get it into the bag), Ceaser's taxes (Mark 12:17), Widow's taxes (mark 12:41-44).
How about a "balance" game with two teams. They each throw into their own cup/bowl/etc and the first to tip the scales past a point on their side gets to split the amount in the cups. (the "house" gets everything that didn't make it into a cup.)
Perhaps you could make a plinko like board with pegs. The bottom slot would have one or two holes marked "charity", "church". Those are the "winning holes". Mark the "losing" holes with "Sloth", "Greed", "Gluttony", etc.
For the signal mechanism, funnel the penny into a location with two wires that connect to a low voltage circuit controling a buzzer. (piezo, or perhaps a relay set to switch itself- parts should be cheap at radio shack)
Other things to consider:
Design the game so that loosing coinage is removed from the playing field quickly. For example, if you use your counter, make the surface sloped so that they slide into a collection bin.
Set up several boards, and only have one player per board.... That way, it's clear who won.
Have limits on how many times someone can win per day.
If appropriate, use different "throw" lines for kids/teens/adults.
Want to be more biblical? Call it a Denaria toss. ;)
good luck!
(I'm starting to think of what i could build for our community fair now. ;)