Hi Adam,
You are right, at least regarding the first (or bigger) of your coins.
It is a Potosi (Bolivia) ½ Real coin; the theoretical weight should be 1,75 gr, so yours is slightly underweight, which for that type of coin is ok.
The obverse shows the monogram of King Ferdinand VI and the date 1758 or 1759 (my guess is 59); the “5” is written in the old Spanish style, which resembles an “S”.
Just to compare, here is my 1755 ½ Real, in which the odd 55 can be seen.

The ID of the second coin is a bit more difficult: no monogram, no date, heavily clipped (quite underweight). But let me try and guess:
turning your coin 90ª clockwise, the three little dots on the obverse will be seen above a possible upper line of King Felipe IV monogram. This type of ½ Real was coined between 1652 and 1666 (aprox.) in Potosi (Bolivia).
An example of my 1662 ½ Real :

Regards
Edit: your 2nd coin cropped and put in the almost right Position
