So, as far as I understand, speakers are basically coils coupled with permanent magnets, then when a current is run through the coil it creates a magnetic field, pushing out against the permanent magnet, moving the diaphragm that's attached to the permanent magnet and creating sound waves.
What I'm interested in is using a coil to do something similar but instead create human perceivable pressure. For example, something to lightly but noticeably push against your finger at a constant rate (not something that constantly moves back and forth like a speaker diaphragm).
If I just make a small coil out of some magnet wire and hook it up to a battery, I think that the magnetic field created by the wire would create a constant pressure against the magnet with the current being proportional to displacement. Is this correct?
If that's right then my real question is if this is possible to do without using a permanent magnet? I know you can create an attractive force to metal with a coil but is there a way to create a repulsive force?
You can either use two coils of wire, or one coil of wire and a permanent magnet. Both will work.
What you are describing is commonly known as a "solenoid". It's a readily available electrical components something like a relay. Go to www.mcmaster.com and search on "solenoid" and you will see lots of commercially available varieties, though most are probably too large for your specific use.
The solenoid is a coil of wire (actually many turns) formed around a circular tube. An iron, but un-magnetized, rod slides into the tube. When the coil is energized the rod (often called the "plunger") will move in or out of the coil depending on the specific design.
So, yes, the mechanism you describe is indeed possible. However, one problem you may run into is battery life. Solenoids are typically current "hogs". In order to maintain the magnetic force on the plunger, the current must remain flowing thru the coil. While current is flowing battery power is being consumed.
If battery size and life is an issue you may have to apply some cleverness to your design and come up with some kind of latching solenoid, probably with two coils - one to push the plunger into the finger and another to pull it back. This way you will only need to energize the coil, and consume battery power, when the plunger is moved, rather than the entire time it is engaged against the finger.