You can use a d6 die for a lot of occasions.
AS A D2: d6 [1-3] = d2 [1], d6 [4-6] = d2 [2];
AS A D3: d6 [1-2] = d3 [1], d6 [3-4] = d3 [2], d2: d6 [5-6] = d3 [3];
AS A D5: d6 [1-5] = d5 [1-5], d6 [6] = reroll.
A coin is not a perfect example for d2, because there is a small chance that it lands on its edge.
The closest thing for d1 I think is the "
Gömböc" (rough translation from hungarian would be "sphery" or "spherette"). It has one stable and one unstable point of equilibrium. (Of course, it is not a perfect d1, since because of the unstable point, but the chances are really small for "rolling" that.)