CSMs are underpowered. 5th edition has seen yet another power creep, most recently culminating in a book where every man is armed with a power weapon. No, CSM are old - they were the first of the fifth and they're beginning to show their age. The few things they have left to them now are Obliterators, Plague Marines and Lash-Princes - these are the few things that hold them up in tournaments. However, even these things are being overshadowed:
Oblits are expensive, easy to tie down with fast assaulters, physically fragile (a good lascannon hit is gonna cost you 75 pts) and you can only have 9.
PM are outmatched by BA Assault Marines, their FNP is relatively worthless against the plethora of low AP attacks in current lists and the focus on power weapon assaults, I3 doesn't do them any favours either.
And that good 'ole Lash tactic is now being countered with the heavy use of mech and consistantly effective Psychic defences. Almost ever list now countains a Librarian/Wolf Priest/Shadow in the Warp/Runes of Warding etc etc, all of which reduce the effectiveness of the one true tactic left to CSM players when our list is so heavily outclassed on every score.
In short, no, there's no way to ditch our only good units and still remain competitive. That would be like saying that non-mech, non-blob Guard could be effective. No, it's not going to happen unfortunately.
You could try going down a route something like
2 Warptime/Wings Princes MoN
Greater Summoned Daemon
2 x 7 Plague Marines PW, 2 Melta, Rhino
6 CSM, Meltagun, Champ, Rhino
3 Vindicators, Daemonic Possession
That's a potential Death Guard army which might have some sucess against opponent with little in the way of anti-armour fire, but don't rely on your opponent picking a bad list for you to win games - it'll be hard fought either way. That list has several tough troops and plenty of S10 AP2 pie plates, PM are as good as our infantry come, and the CSM are a caddy for the list's third monsterous creature. This means that you opponent will have 5, and then eventually 6 high priority targets to aim his high strength weapons at, all of which can pose a great threat to both this line units and his tanks.