Standard sprite size on the C64 in high res mode is 8x8, and you can't use more than two colours within that space, should be serviceable.

C64 sprites are 24x21 pixels in 1-bit monocolor (foreground color + transparent), or wide-pixel 12x21 2-bit multicolor (3 colors + transparent).

Character size, not sprite size. Sprites are bigger, but you can (officially) only have 8 on screen at once. Clever scanline-timing tricks can increase that to a few dozen before flickering sets in, but still not enough for general use emoji.

Redefined characters would work, but they're limited to a total of 256 characters at a time, including the usual letters/numbers/punctuation. Still, 150 or so of the most popular emoji would go a long way!

Sprites are 24x21, characters are 8x8 :)