Sure can. Kids are amazingly resilient. I grew up with my mom and used to visit my dad on weekends. It was stressful and tough at times back then but now I think it helped build character. It's important for children to have a loving, nurturing home where they feel safe and secure. This can happen with two parents, one parent, two grandparents - whatever.
A child can become emotionally stable when brought up by a single parent. However, this will depend with the strength will and virtues of the parent. Weaker parents tend to evoke emotions of regret to children causing them to be emotionally unstable through their lives.