Arrowroot? Not sure exactly what it is but I know it's vegetarian, you buy it from healthfood shops and use it to thicken things without them going 'opaque'. I think you use it like cornflour, ie slake it in water and mix it into the coulis.
Potato starch (often sold under the name Farina) would work. You mix it with a little water just off the boil, and then blend it with the coulis. You mustn't actually boil the starch mix, as that will stop it setting.
If you're happy to cook the coulis, then a knob of butter will thicken it, or, of course, some cornflour.