Short answer: such a printer does not exist (at least not as far as I'm aware).
The reasons are the precision required for the common printing technologies and the price dumping in the consumer market. Manufacturers must sell hundreds of thousands of their printers to make a profit. Printing in a bound book is such a nice scenario that there's simply not enough money to make.
In ink printing the printer head (where the ink comes out) must be a precise distance from the paper away. The printer head is also very small, so it has to move over the paper from side to side repeatedly to cover the whole page. If the page is bound in a journal, you'd need to press it as flat as possible, which might damage the journal. The printer head would also need to move up and down because the first page is higher than the last page. This kind of technology is certainly possible, but would be too expensive for the consumer market.
In laser printing the page must be negatively charged. The laser then discharges every spot that's supposed to stay white but leaves the remaining charge in the spots that are supposed to be black. The prepared page then passes in front of the toner cartridge, where the remaining negative charge attracts the toner particles. The page is then heated up to melt the toner into the paper.
Again, it would certainly be possible to achieve this in a bound book, but it's much easier and cheaper to move the paper over the components than the components over a bound book.
For a journal I would use thin paper. Packages of printer paper usually have an information about how heavy the paper is. The standard office paper is 80 g/m3 (grams per square meter), but you could easily go as low as 60 g/m3. At 40 g/m3 you have things like plotter or parchment paper, which might work, but might not be what you want. Anything lighter than that is probably more like tissue paper, which smudges in an ink printer.
To glue the paper into your journal, you should use a spray glue instead of liquid glue to avoid warping. Glue stick also avoids warping, but can leave behind bumps of uneven glue. It can also help to put something really heavy on top of the journal right after glueing, like several bricks heavy.