This is an interesting scenario. As a trainer and as a person who works out, I understand the importance of goals. I also understand the importance of those goals being attainable. The trick is to figure out what is attainable and what isn't. In the military, there are different requirements depending on the age and sex of the person. Women are required to do a certain amount of a given exercise, but it is usually less than the requirements of the men. (In the Marines, I believe they use the term "physical readiness test" for their fitness evaluations, but I'm not sure).
Also, I'm not sure if Marines require pushups(like the Army does), or if they require pullups, which may be the case.
So, if MAIN goal is to join the Marines with pushups being the defining factor, I would do my best to progress them to meet the minimal standard necessary.
This means taking the person from where they are(wall pushup,all fours,etc) and progressing them in the shortest time possible to a full pushup without injury. This can be tricky and would come at a price of not getting a full body workout because the workout would have to be so focused. I would make sure the upper back is strong to counteract the exercise so for each chest exercise, I would do an upper back one. I would also add core work to make sure they can stabalize themselves during the movements. I think that adding some plank work(on the forearms and the hands) would be really helpful. Side planks may also help to activate the Serratus Anterior which will help with good form.
IMO, the only way to progress with pushups is to do pushups. This may require working the person to extreme muscle fatigue(like getting them to add one pushup every or every other workout, or doing as many pushups on the toes and then doing as many possible on the kness,etc). But like any resistance training, rest is necessary, so this goal may take quite awhile if it's going to happen.
I wouldn't promise the client that it could be done though. I would only promise to do what I could to help progress them to their fullest potential. This may mean that the goal is unattainable, but I would do my best to be honest and upfront about it from the beginning. I'm not sure this answered your question but it's what I came up with off the top of my head. Would you change anything or do anything differently? Just wondering.
Carolyn