Playdate for my daughter

Hello- my name is Amy- my daughter and I are looking for some friends! Basically my poor baby don’t have any friends her age to play with. My daughter is 7 almost 8. We usually have allot going on, I have a son too thats almost 11, he has plenty of friends, but loves making new friends, but my rant or post today is to ask how do kids make friends to have play dates- I’m that mom that is literally watching both my kids at all times, 99.9% I’m playing and doing what they doing. So I’ve caught my daughter begging her one little friend to stay and play, and just hearing my daughter beg her melted my heart! You don’t beg anyone to be friends with you! My daughter is very very social- last night was the straw for me- she asked the little girl to come over today and have a play date, and she tells her I’m going to my other friends house, all she does is rub in my daughters face she has other friends! I get it, but the way she says it, is just mean, all she wants to do is have a friend! So here I am asking how do I get her friends- my son was so easy and still is. Anyone interested in having a play date? I have all kinds of stuff to keep kids entertained. I don’t know, just feel bad for my daughter being 2nd choice. So figured I would post on here :) Thanks for listening to my rant.