I've been using a small syringe for prime, and it's been working pretty well for me.
I've also seen some people recommend these little syringe adaptors that push into the neck of the bottle, and the bottle cap still fits over them, but I haven't found any yet. I got a similar product, a stopper with a small syringe-sized hole, but it's not a very good fit, and has to be removed/replaced each time, so it's more difficult then just sticking the syringe into the bottle.
There's a TAP plastics near me, and they have various pump tops for different sized bottles. If there is a plastic supplier near you, it might be worth poking around and seeing if they have something similar. Or maybe just use one from a bottle of hand sanitizer when it runs empty (might be able to use a soap one, but it would probably take more cleaning).