Georgievna? (it's closer to George but I can't think of anything else)
Are you sure that you want to do this though? After all, you can always call your child this without it actually being the official middle name. I wish I could get rid of my "middle name" from official documents. Have you considered giving a middle name that's either your mother's or grandmother's name? (I take it you're having a girl?) That way you still preserve the heritage but it doesn't complicate the child's life too much :)
Did you also want to give your child a Russian first name?
The most common names for girls are Irina, Natalya, Maria, Anna, Ekaterina.
Go here or just google "russian baby names" for more information.