My tyre changing kit is a bit Robinson Crusoe but it works.
I use a square wooden frame covered in carpet to put the wheel on, and some toe-down straps. (I need to make a new frame as my old one is in the UK!).
I have some plastic rim protectors and 3x tyre irons.
To break the bead I use a garden spade - just jump up and down until it goes. A bit of WD-40 helps for stubborn tyres.
Then just use the tyre irons and the frame to get the new tyre on.
Done loads of tyres like this, it's not too bad when you get the hang of it.
That said, if I could find a decent, CHEAP tyre changer I would get one.