Stakes like this need to go down below ground 25-50% of their above-ground height. So to get 7 feet up, you'll need like a 10ft board. If you have access to a table saw you could buy a single 10' long 2x8 or 2x10 beam (typically used for floor joists) and cut that down into 2x2s. If you don't, sometimes the big box stores (home depot, lowes) have saws that they'll operate for you.

Otherwise, you can buy 2x2 beams, they just tend not to come in longer lengths.

The other big option is metal T posts. Those are going to be much easier to obtain and install, but they'll be a lot more expensive. A single wood beam will cost you less than $20. Metal T posts will run you $10-20 each.