think your best bet would be to buy some tanalised (pressure treated) battens and screw the vertically to the fence (presume its waneylap so screw to the laths (battens) , one either side and one in the middle, then screw the trellis to the battens. very low cost and a decent job , i have done it many times. if they are large trellis put battens front and back of the fence
