Is cheap, smooth, digital sound possible?

I've recently gotten into vinyl playback and have grown to love its very smooth, warm sound. I only have a few CD players in the house, none of which I would consider "smooth." They are a Sony DVP something (cheap DVD/SACD player), and an NAD T532 DVD player. I've tried listening to music on my iPod which sounded a bit more laid back, but still caused listening fatigue after a short while. Is it possible to obtain a cheap player/DAC that will have a nice, warm sound that won't give me listening fatigue so easily?