This lemon chicken recipe is fantastic. It is best made a day ahead and is good hot or warm, making it a good choice for a picnic.
www.seriouseats.com/recipes/2007/05/cook-the-book-lemon-chicken.html

A simple dish would be to take a roasting (or frying chicken), grab a couple of those lemons and puncture them with a fork. Stuff them in the cavity. Add fresh sage or tarragon under the skin. Truss it up just a bit to keep the cavity closed. Rub the skin with olive oil and sea salt and roast. Meyer's go really with almost anything chicken.

I make this with Meyer Lemon ... the nice thing is you get to eat the lemons. Also Lazy Mary's Lemon Tart on this site!

http://www.food52.com/recipes/3297_roasted_chicken_with_honey_lemon_and_rosemary

I would definitely make this pie for a memorable use of your meyer lemons. It only calls for 1/2 cup of lemon juice so you will also be able to make other recipes. www.epicurious.com/recipes/food/views/Lemon-Ice-Box-Pie-109558

Lemon curd. Lemon curd. Lemon curd. Fine Cooking has a great recipe. It is hard for me not to eat it all right out of the jar on a spoon or my finger. I can try and access it if you can't find it. I just can't get to it from here.

This is Merrill's recipe, and I like (love) it just as well with Meyer lemons as I do with limes.

http://www.food52.com/recipes/5438_the_best_lime_ice_cream

Try mrslarkin's wonderful winner, "lemon posset" a simple but spectacular dessert. I have a Meyer lemon tree and this is one of my favorite Meyer lemon recipes!

Risotto, Marmalade, Thomas Keller has a cured Meyer Lemon treatment that can be used a number of ways. Really any way that you can showcase the flavors of Meyer Lemon would be great. Personally, a roast chicken with a compound butter of Meyer lemon zest, salt and pepper tucked under the skin and a couple lemons themselves stuffed into the cavity would be my pick. You could also use Meyer lemon in the accompaniments like a Rice Pilaf or aforementioned Risotto. Just my two cents.