Most modern, inexpensive, single-disc CD players have "Blu-ray" written on the outside
Unfortunately, finding inexpensive ones which also have analog outputs (let alone quality analog outputs) could be a problem.
Onkyo has several current-generation changers that can play CDs, which seem to be reasonably inexpensive, though. e.g. their DXC390 6 disc CD player as sold by Amazon is only slightly more than half your budget. You might want to consider something like that, since you'd get a full manufacturer's warranty, too.