We have a Older mobile home with an outdoor weel cap, there is no pressure tank, we are experincing rapid cycling issues.. how do we get pressure back into this system?

I have heard of wells which actually have a pressure tank inside the well, though I have never seen one. I would think you could simply add on a tank. Even if it turns out to be a second tank, I don't see why that would cause a problem.

Is your pump above ground or in the well?

I, like jlisenbe, have heard of this type of well system but never seen one. It requires a special pump that is capable of sustaining the constant switching on and off. Each time you use water the pump must turn on to pump the water. Logic would say that there has to be a pressure switch on the house side of the pump.
If you have lost pressure the switch may be faulty or need adjustment. It could be that the port of the switch needs cleaning.

It could also be the pump wearing out, lets hope not.

Suggest that you turn power to the switch off, remove it from the piping and make sure that nothing is clogged.

Considering the type of pump HK just described, adding a second tank might not be a good idea. Hard to say.

I guess that I was not quite specific enough. There are well systems the do not use a tank. You simply rely on the pump to come on each time you open the faucet. Pump has to be rated for that kind of service.

I can't see any reason not to add a tank. It would certainly add to the life of the pump.