Welcome to the site and to this thread.
I am presuming that you mean the liquid is coming out as you are trying to put it in, which is a problem that I have.
One of the things about stomas is that not many people know what is happening on the inside of their stoma so it is more difficult for them to find a solution to this sort of problem. Right at the beginning, my stoma nurse stuck her finger deep inside mine and told me which angle I should be pointing the cone in order to avoid 'splashback'. I thought right there and then, that if she can put her finger in there, then so could I, which would enable me to know exactly what I'm dealing with.
In my case one of the muscles close to the stoma exit was closing over the hole completely and not allowing the water to get beyond it. I found that by persisting with my finger in there and exerting enough pressure, the muscle eventually relaxed and let my finger pass further in and there was no obstruction beyond that point. At first, I could just about get the cone to go in as soon as I pulled my finger out but I soon realised that the cone was simply not long enough to get passed the obstruction.
What was needed was a longer tube, more water, under more pressure than the hanging bag system provided so I got to work devising a suitable, simple system just for me!
I used to anally irrigate before my stoma so I knew that there exists a suitable 'sized' anal catheter, which was unsuitable in design because it also had an air balloon to stop the water escaping. I cut the end off the catheter and fixed it to the end of the tube coming from a pressure pump (this was a garden sprayer). The tube also had a control valve - courtesy of COLOPLAST who make the irrigators. To stop the splashback, I made a plastic shield (out of a suitably shaped bottle of bubble bath) through which I drilled a hole and threaded the tube through. This enables me to adjust the length of tube that goes into the stoma. All the splashback hits the shield and goes harmlessly down the sleeve.
I've been using this system successfully for over a year now and what I have found is that once the water input has begun, I get the splashback for about 30 seconds or so and then, I'm presuming the muscle contracts around the tube because the splashback then ceases until I pull the tube out when I've run out of water. The pressurised garden sprayer I use holds 3 litres, which is enough to allow for the loss or water due to splashback.
I know it may all sound too complicated, but the device is really very simple and easy to make. It also might be a bit difficult to envisage the gadget just from a written description, so I'll try to post a photo on my profile when I get time.
Braun Medical do a pressurised system for irrigation but I found that it did not have enough water to compensate for splashback, which is why I opted for a garden sprayer as they come in all sizes Up to several gallons!
Don't give up on irrigation just because there are teathing troubles as there is usually a way around the problems if you can identify precisely what is causing these issues.