Yes, self-inking stamps can be refilled with ink. Many self-inking stamp brands offer refill ink bottles or ink pads that can be used to refill the stamp body. It's recommended to follow the manufacturer's instructions for refilling to ensure proper and safe use of the stamp.
You can purchase this customised self inking stamp here
The refill for this self inking stamp can be purchased HERE in a variety of colours.
Self Inking Stamps can be completely customised to include your company logo design or you can buy Self Inking Stamps off the shelf. A Self Inking Stamp is a single unit containg a rubber plate and ink pad. When pressure is applied onto the handle an internal mechanism releases the design into the ink and then when applied onto paper/card/skin prints an impression of the same design.
A Self Inking stamp is more portable than a separate ink pad and stamp but for that reason can be slighltly more expensive.