My review of the AmazonBasics Remanufactured Ink Cartridge Replacement for Brother LC51BK Black through the Amazon vine program is available at Amazon.com here.
I presume that there are many such cartridges available for many different types of printers. I got this one because I have a brother printer that by an odd coincidence was about to run out of ink.
Great timing that.
Da Techguy's (no longer backup) Blog 
I used to refill my ink cartridges back when you could still do that. I stopped after I went on an interview and there was a slight drizzle. My resumes smeared very badly. Fortunately I had extras in the car. But the original inks did not smear like that.
Maybe things are better now.
Brother LC51BK Black Ink Cartridge can be used to print a few sheets?