Sun or shade? Dry or wet? As a ground cover or more mounding?

Ilex crenata Touch of Gold® ('Adorned') would eventually need some minor pruning. Similar to 'Drops of Gold'. 'Golden Hellerei' may work for your region. It doesn't get quite the gold up in my area though.

Abelia ''Lemon Lime' or 'Miss Lemon' would eventually need some easy tidying up.

'Mojo' and Cream De Mint® Pittosporums are not really gold, but have a cream-edged leaf. Nice evergreen though. perfect small mound. Not sure what deer think of it.

For dry sun, 'Mother Lode' juniper is nice. Deer and drought proof.

Some of the evergreen Daphnes can approach gold edge, but probably more cream-edged.

For well-drained part sun, you could try one of the golden Heucheras (Corel Bell) like 'Electra' or 'Lemon Love'. There are many gold varieties out there. Heucheras are perennials and not shrubs though.

For arid, hot and dry, consider Yucca filamentosa 'Color Guard'.

'Lemon-Lime' Nandina is industrial. Newer growth is gold. Sterile cultivar.

More a low ground cover, Ajuga tenorei 'Cordial Canary' and 'Tropical Toucan' have chartreuse foliage and blue flowers.

Numerous Hostas are golden, but the deer.

If you like conifers, there are a number of small mouding Chamaecyparis such as 'Night LIght'.