get google play store on my pc to recognize amazon fire tablet

[AC Question]

I bought the amazon fire tablet (8""). I installed the google play store on it. I have no trouble downloading apps when I access the play store through my fire tablet. however, I prefer downloading apps from play store to my tablet via my pc. So much easier. the problem is when I try to download an app from play store it recognizes my note3 and my nexus 7. I have tried everything to try to get play store to also recognize the fire tablet. Can it be done???