Super glue and masking tape on the base and then maybe set up a clamp block either side and some strips accross the top where you are not engraving.
I keep meaning to get a set of those engineering step blocks and threaded bar for this sort of thing but always end up using random blocks of wood.
To find the centre there are several ways, a probe would be best but you can do the same without one by jogging till the bit touches one side zero it, move it to the other side and note the dro reading, do this a few times ( 3 points at least ) then you can work out the centre.
The way I would probably do it (because I am super lazy) would be to put a few strips of masking tape over the top and mark the centre with a normal centre finder then use that to find x and y zero. Do z from the rim surface.
The ‘proper answer’ would be to use a rotary system - I have one for the laser and it will turn the bowl / cup as it engraves - if you don’t have it turning then only the very top bit will be an accurate depth as you go to either side it will become less accurate…