Can someone convert the ingredients from grams to cups please?

Kaitlyn, I agree with the others that using a scale and weight measures are the way to go for baking--especially for batch-to-batch consistency. But since your question wasn't about the merits of weight vs. volume, you asked for a conversion and I like playing with baking math, here's a close approximation with a few close roundings to get to reasonable volume measurements:

Coconut Linzer Cookies with Rasberry Jam
9Tbs butter
6Tbs + 1tsp caster sugar
1 egg
1tsp vanilla extract
1+7/8cups plain flour
5/8cup desiccated coconut
1/2tsp baking powder
1/2cup raspberry jam
icing sugar, to dust

Bake on!

Kaitlyn716, Looks like a great recipe, but I fully agree with PieceofLayerCake about purchasing a scale for your kitchen. I might add you are asking for conversions of weight (grams) into volume (cups). Every ingredient most likely would have a different conversion rate, ie. by weight, 100 grams of flour would fill a larger space than 100 grams of raspberry jam, by volume, a cup of flour is lighter than a cup of jam. Baking recipes really do work best if measurements are by weight rather than by volume.

There are a number of resources online that can assist (to a degree) with this task....but, I would be remiss if I didn't strongly suggest you find a nice inexpensive scale for this recipe. It will come in handy in the future if ever you desire to make these again (or any other of a number of fabulous recipes that are written according to the metric system).