If I have a method that requires a parameter that,
Count propertyWhat should the type
You are out of luck here. IList doesn't implement IReadOnlyList. List does implement both interfaces, but I think that's not what you want.
However, you can use LINQ:
Count() extension method internally checks whether the instance in fact is a collection and then uses the Count property.ElementAt() extension method internally checks whether the instance in fact is a list and than uses the indexer.