There is really no such thing in Oregon as visitation rights solely based on the relationship of being a grandparent. Oregon had attempted to create Grandparent visitation rights in the past, but the statute creating those rights was repealed after the landmark decisions in Troxel v. Granville,530 U.S. 57 (2000). In the Troxel case the United States Supreme Court determined that parents have a constitutional right to rear their children free from the intervention of the State or a third party under normal circumstances. There is a presumption that a parent acts in the best interest of their children so a parent's decision to limit visitation with a grandparent is presumed to be correct until proven otherwise and in examining the parent's decision the court must give great weight or great deference to the parent's decision and right to make that decision.
The right of the parent comes first but may be limited if there is a showing the parent is not fit to make decisions about their children or that they are not fit to parent their children. (ORS 109.119 lists several factors that the court must consider before it can override a parent's decision.) One must understand that most parental decisions will be upheld by the court due to the great weight that must be given to the parent's decision even if there might be a better way to raise or parent that child. Parent's don't lose their constitutional rights to parent their children just because someone else may have a better idea on how the children should be raised. So even if the intervening party that wants custody or visitation can show that they could offer the child better care or a better life, this would not be enough to force the biological parent to turn over custody or allow visitation. It is not about the court considering whether a grandparent or another person could do a better job then the biological parent. It is about the parent having a superior constitutionally protected right to determine how they raise their children and who their children associate with. This right of biological parents cannot be easily disturbed.
Following the decision in Troxel. Oregon enacted a new statute, ORS 109.119, which is frequently called the "Psychological Parent" statute. Essentially, this statute gives people that have developed a very close, almost parent like relationship with a child, the right to Petition in the court for custody or visitation with the child. This rather complex way to ask for visitation or custody is covered by ORS 109.119. Your can read the text at this link: http://www.oregonlaws.org/ors/109.119 Pay attention to the definitions in the statute that describe two types of relationships that can give rise to a right to Petition in the court. One is called a Child-parent relationship. The other and less significant relationship is called an ongoing personal relationship. You need to have the facts in your situation which show that you have established one of these types of relationships to qualify to seek relief using this statute. The language of the statute has been interpreted by court decisions that need to be read to fully understand what type of relationship would qualify and what type of relief that court is likely to allow. So it is going to be necessary to talk to a family law attorney to figure out whether your situation will qualify and to get an idea of what you might expect the court to order if you file a petition.
Absent establishing a very close relationship as defined by ORS 109.119, that would give rise to the right to petition for visitation or custody rights under ORS 109.119, grandparents normally get to see their grandchildren when one of the biological parents brings them to visit. So the path of least resistance is for grandparents to work with the biological parents and set up the visitation.
To determine if you have any rights for court ordered visitation under ORS 109.119, you will need to consult with an attorney. If you don't yet currently have the requisite relationship, an attorney can help you understand what steps you might be able to take to build that type of relationship so you can apply in the future. Keep in mind that at least one of the types of relief you can seek under ORS 109.119 requires that your case has to be filed within 6 months of the time period when you had the requisite close relationship with the child. So, depending on what part of the statute applies in your situation, you may need to file within 6 months of when your relationship with the child began to change. In other situations you may have more time, but the safest course of action is to speak to an attorney right away so you don't miss an important deadline for filing.