The archers ring is the best ring that you can get for the skill Range.
The ring can be obtained from the Dagganoth Kings, These are hard to kill as they all 3 of them attack you at the same time all using a different skill, 1 uses Range, 1 uses Magic, and one uses Melee. The ring is not a common drop so it is hard to obtain. It is best to go in teams so you have more of a chance of either getting one or you stay alive for longer. The dagganoths are located in the "boss Teleport" when teleported there climb down the ladder ready.