If you had it before and loved it - tell the docter you want it.
Depo shots can cause osteoporosis and are not good for long term in my opinion because of that. As well if you do want children it can take up to 2 years to get your periods/ovulation back on track. I was on depo and they told me none of this. The pills is okay, but you have to remember to take it each day.
Unless the expense is beyond what you can afford - I'd go the route that was working. And as far as expense goes if you add up the cost of birthcontrol over a 5 year period - probably cheaper than that.
Perhaps the doctor isn't comfortable inserting it and doesn't want to admit it - I'd ask to go to an OBGYN to get it inserted.
If you don't ever want any more children - you could ask your partner to get a vasectomy. It is a day thing, and then you are 100% sure there will be no babies. You could get your tubes tied but that is a more invasive surgery.
I would personally tell the doctor you thought it over and still want the mirana. See what they say. Although make sure you get it replaced after the 5 years. I had a friend that got pregnant with hers in. Her son was actually holding onto it when he was born. As if to say "Ha ha - thought you were safe did you? Well here I am!"
If you don't want to take birth control pills the depo shot I've always had good luck with. It depends on the person of course. It lasts for 3 months and I had no periods on it after a couple months. Congrats on your baby! We are just starting our journey at 5.2 weeks, our first child.