If you're asking how to introduce the subject or how to share your faith... that depends on who you are and who he is. If it's forced, it may not do much good, because like you've admitted and others have suggested it may feel to him like you're forcing religion on him rather than sharing something that is beneficial to you. I haven't dated anyone who wasn't Christian, so I'm not really sure how to respond to that part of your situation, but I'll share what I think regarding witnessing and you can take it as you like.
When I'm witnessing to people I know personally, I usually take it slow. I don't introduce the subject, except as it comes naturally to me. I am a Christian. I don't in any way hide from that fact or the convictions and beliefs I hold because I follow Christ. I am very open with that, because it is a very significant part of who I am. But I don't often talk about it in a way of trying to convince others to be the same way. I share in casual conversation. For example, at work there's a lot of gossip sometimes. Whenever my co-workers try to get me in on it, I simply say that I am not a fan of gossip and would prefer to think and speak kind things instead. If they ask why, than I have an opportunity to share deeper. If not, they still identify me with Christian values. I have actually had several co-workers ask me what I believe and than I have taken the opportunity to share with them. In those instances, I try as much as possible, to share Jesus first. To share not just who He is, but who He is to ME. Why I care. How He benefits my life and gives me hope for the future.
So I guess the best advice I could give is, just be yourself. Don't hide who you are. Be open with your beliefs as they apply to you and how you view the world around you. Stay connected with Christ and with your faith community. Don't hide for fear that you'll push him away from God or from you. You don't have to be confrontational about it, but don't hide it. The best relationships are based in mutual availability and trust. Whether or not he's a Christian, if you can't trust him with who you are than the relationship won't work out. Likewise, if he can't trust you with who he is the same applies. Just show him Christ's love for you. Christ has a way of drawing people to Himself. Don't worry about convincing him, because that is not your job. Your job is to be open, to be yourself, to follow Christ no matter what. The Holy Spirit of Christ has the job to change hearts.
