I'm glad to hear that she's 2 years old. Good job on your part in waiting until she's physically mature enough to do this.
The male may still be rather young. Many breeders prefer waiting until the male is also about 1 1/2 to 2 years of age.
Here is more help for this subject http://www.k9web.com/dog-faqs/breeding.html
and this site is also helpful
If you are going to continue:
From the first day you see spotting (bloody discharge from the vulva), count about 10-12 days. This is the approximate time the female will be ready to stand and mate (accept the male).
Introduce the male a few days before your records (counting 10-12 days) indicate she'll be ready. You may have counted wrong and she may have other plans. Also, these are just general guidelines which may be different depending on breed of dog.
Never try to force a mating pair together (when she's ready, she's ready and not one hour sooner). Try to keep them together for 3 or 4 days or until she no longer stands for him.
Depending on accuracy of owner calculations, delivery should be in 59-66 days. 63 days is average.
It's nice to hear that you own and care this much about them both. I'm really happy to hear that they are important family members rather than just pets.
If the female won't stand for him, there's not a thing anyone can do to change her mind. Mother nature has control over this. Even the dog doesn't have a clue as to why she thinks she wants him, then doesn't allow him.
Since they live together you might just want to leave things be and happen in due time, although monitoring them is important in order to be sure there's no fighting (this too would be by nature, not by their choice) and to note when a tie occurs (in order to determine a due date).
The male may just need some more maturity.
As an owner of an animal rescue org, I have to mention that there's a higher risk of disease, a shorter lifespan overall and other health complications in intact dogs (non spayed/neutered). This is something that many owners don't realize and once their companion develops cancer or something else, they wish someone told them when they still had time to make things different.
Look at this http://www.peteducation.com/article.cfm?cls=2&cat=1625&articleid=911 and this one is pretty important too http://www.hppl.org/BasicNeuteringInfo.htm
If you didn't know this, it may make a big difference.
Good luck either way and really, keep up the good work!
Another of our experts has a suggestion to separate them for 24 hours and see if this makes a difference. Jadedangel is one of my good friends as well as fellow expert here, I completely respect her advice.
I'm sure you're doing all the right things and I hope you understand I just had to mention the other stuff. It really is just an obligation I have and now that it's said, I encourage you not to give up on these two. Give the 24 hour separation a try and check back with me ok? I'd love to hear a 'baby announcement' in 63 days