Mailing out a gift?

i think either one would work

Twenty minutes away? Can you tell her your mom is driving you at a particular time and then drop off the beautifully wrapped gift at the front yard? Then you can wave, yell happy birthday and tell her that you miss her. Alternatively you can send an e-gift card. Remember to text a happy birthday on her special day. 

I suggest a card with a small amount of money ($5?) and notice to watch for your gift of a magazine subscription. Nothing to wrap and no trip to the post office. 

What would you usually do, if you weren't mailing what you give her? Do that, assuming that the gift is small enough to mail without effectively paying twice for it.

On the other hand, if it's going to cost $20 to mail a $20 gift, send money and she can buy herself a $40 gift. DO NOT send cash in the mail. It often never arrives. Send a cheque. Or an e-transfer, or a money order.

Either a gift/birthday card or if your cousins' parents have paypal send $ that way.

Send a gift card.  It's easier.

You can go on a site like Amazon, buy a gift, and have it shipped to the gift recipients home with your name on the gift as the giver.

On the subject of cash gifts, it may seem informal to you, but you should consider what makes the eight year old happy. It could be her first opportunity to spend her own money, like a big girl.

You never ever send cash, chances are that it will not get there, just buy a gift, wrap it well in strong brown paper, address it clearly, take  it to a post office, they will weigh it and tell you how much it will cost to send it, allow at least 2 weeks for it to get there, the post is up about 60% at the moment.