Make a GameObject more stable in Unity2D

Hi,

I wanted to make a sort of 2D runner in unity and this game to be fast (I mean like sonic for example). But the problem is that the player is overturning. I would like to make it more stable but not by using fixed angle. So my idea was to make sub-objects of the player with differents masses, heavier for the bottom and lighter for the top. I tried different ways but it hasn't worked yet.

So my question is : Is there an other way to make it work ? Or is that way the good way and then how to make it work ? Or is it a good idea to want to make him stable or is it an other solution to do a runner.

PS : I work with unity2D so the problem is not the same as unity3D I think.

Thanks !