We have a coffee maker that keeps needing to be refilled. I had an idea to split of the ice maker line (which is easy) to supply the coffee maker. The only issue is, is there any attachment that with a press of a knob or nozzle water can be dispersed? This would have to fit the regular sized ice maker lines. Thx.
The problem with your idea is the risk of damage of the line and associated leakage.
While ice makers use thin copper or plastic lines, they are permanently attached and not handled once installed. The valve that controls the filling is built into the ice maker, and is automatic.
A similar approach to your coffee maker would require that you have a fixed mounting for the valve that is substantial and protects the line and attachment from rough handling. There are such systems used as pot fillers, like this one
These are permanently mounted on a wall very close to the point you fill pots, such as a stove. The risk is spilling water in an area with no drain. These units are usually installed with standard plumbing (copper, pex, etc.), not lightweight tubing, although adapters probably could be used to accommodate small tubing.
While there are small plastic valves that are used on things like water jugs, these are also intended for fixed mounts of the valve.
You can add a typically kitchen side sprayer (probably has some actual product name too)
It will not have the same connection as your ice maker line but you can buy adapters. If you have a flexible line (or T off to a flexible line) you can probably cut the end of off the sprayer line and get one barbed connector as your adapter.