Dunno, need to know precisely which conifer it is - if it were, say, a leylandii cypress, no. the other consideration is the increased possibility of fungal infection on the rose (mildew, black spot) because of the lack of airflow with a dense, evergreen support. Open situations with plenty of air are best for roses - even a deciduous tree would be better.

I agree with Bamboo,the only way you could grow a Rose on a conifer i.e. leylandii is to cut off all the growth on the face side, cover with garden netting, buy a large rambling rose, plant away from the roots and see what results you get. I have a climbing rose growing through a holly tree which is 40ft. high.