How can you assert your estimation so confidently without even knowing how big the tiles are? They can be done "easily" AND "as beautiful as possible?"
By assuming the worst case scenario (32x32, few recolours) and making a realistic estimation from there.
Cartoon styled tiles are excellent to work quickly on because you can block out a large chunk of the tileset in one go (say, all the tiles for a grassy area), quickly outline and two-tone shade any required forms (for our example, rocks sticking out of the ground, larger clumps of grass, some larger stone blocks and bushes, etc etc) so you can build a small mockup using all required tiles. From there it's easy to pick what forms don't work and where more variation is needed. From 1-2 hours work, you've then got a rough draft you can send to the client, and while you're waiting for feedback you can start on another part of the tileset.
The only thing that would make that take longer than a week is if he required some larger objects with various facing directions to match the tiles, or animation in some of them.
I can't work full time either (full time uni student), but I can draft ~8 original 32x32 tiles in an hour and polish them in 3, so I suppose I'm just under the 2.5/hr level. For smaller tiles (What I'm better at) I expect that count could be quite a bit higher than 2.5/hr though.
Getting feedback
before you've done the hard yards (optimising those clusters, tweaking colours, etc etc) lets you cut down on wasted pixelling time a lot, so I think 1 week is reasonable for 50 tiles with some copypaste variation tiles, but because of possible revision issues I'd quote a longer time to a new client to give myself some breathing space.
If I was working with someone I had experience with (and therefore knew more accurately what they wanted) I'd give them a less lenient time frame.
It's all pretty context sensitive, but from what I've heard from DaCarterMan in a Personal Message just now I wouldn't have been too far off the mark with his requirements.