Morphine is an interesting one. If you're already into injections, it's pretty solid. Pretty much every other route of administration is going to pale in comparison. However, it is not advisable for anyone not already in that life to take it up just for some kicks.
I still advise rectal administration as the best route absent of injection. You want to hold onto a piece of knowledge here that is important. The lower portion of the rectum i.e. the part closest to your butthole (sorry for the crass language) is much better at absorption than the upper reaches of your rectum/colon. If you want to take advantage of this fact, than you need to administer your solution, ideally no more than 3ml-5ml for this purpose and then make yourself upright, letting the solution be absorbed by the lower reaches of your rectum. This is in opposition to typical technique, which would have you laying on your side for administration.
There is limited data on this subject, but enough to make some judgement. It seems that when the Morphine is administered in a viscous solution, absorption tends to be better. I had read this same paper years ago when I was in the same position you find yourself in now. I adapted based on this research and found what I believe to be the most effective method of rectal Morphine administration.
I would crush my pills first. I would take a miniscule amount of water, just enough to get the pills into one step beyond a paste. Then, I would take coconut oil, though I feel you could use any cooking oil, anything fatty, for the same method. Take your solution of Morphine pills/water and combine them with no more than 5ml max of your fatty substance. Mix well.
Draw everything up into your syringe. Directly before placement, give it one more good shake. Insert and depress the plunger. Now, as you wait, either sit upright or if you can, go about your business. It should not take longer than 20 minutes for every bit of it to be absorbed.
I know it's not pretty, but that's the situation with Morphine. For the record, when the formulation and administration are correct, you should expect a significant deal higher than oral administration.