Your idea of wanting to achieve a permanent anal gape must be the sexiest thing I have read on here. Like it's been said, I don't think that something like this is possible - but you can hold your asshole open for a considerable amount of time if you had enough training and your muscles "understand" how to behave. You can have a very lose asshole no problem just by fucking it or having yourself plugged with ever bigger objects but that is not the same as a gape. Some are just not built to have a real gape too, their asshole might be open but for it to be a real gape your inner muscles have to relax too and a tunnel has to form that goes into your butt. I can show you some examples in PM if you want.
Would be very much interested in your progress and what else, if not only the dares you are doing to achieve your goal.
Like the first replies I too would recommend you the stretching rings, sounds like they would be perfect for you. Or if you could somehow manage to get your hand to work on your ass, it would be the best tool really.. and it's free. Not that I don't believe you are not flexible enough but sometimes things you think are not possible can be if worked for hard enough. Just like your gaping wish. Maybe you can make it a secondary task.
My dare for you till then is to get an eggplant of a size that you will have to stretch your ass to get it in to its widest part and doesn't slip in too easily. Before using the eggplant you can warm yourself up with anything you have been using already, like an apple.
Now if you want to have a gape - no permanent gape yet.. get on your knees and get in a position you can fuck yourself comfortably for a while. Spread your legs apart and put your head on a pillow or something similar. Important just is that your head is always lower than your butt. Basically the face-down-ass-up position. Start inserting the eggplant and push it in slowly until you are past the widest point. Keep it there for a few minutes so your ass gets used to the penetration. Then start fucking yourself with it, first very slowly and always pulling it out completely. You might push in some air when re-entering your asshole but that will actually help you gape, if you don't like that feeling just push the air out though gaping will be harder. Gradually increasing in speed start spreading your cheeks apart while fucking yourself. It is important that you have your asshole spread as wides as you can because it supports your gape. It might take a few tries to get a technique to do this with one hand (two hands would be preferred for this :-). Once you are up to a speed of inserting and pulling out the eggplant say once every second, start having smaller pauses before getting it back in - always while you are spreading your butt-cheeks. At some point your gape should stay there expecting a large object to come back into your ass. If you're good that might be up to a minute.
Do this for as long as you want and you are comfortable to get a gape if you don't see any results right away.
Hope it will help you a bit. And a reminder that is for everyone playing with their asses, not just opennina - keep it on a safe level. That means good lubrication, nothing that could break in your ass, get lost or injure you in any way. It has been said before but it should never be forgotten.