Ask Mr. Smarty Plants

At this point, Mr. SP decided it was time to contact the butterfly/caterpillar expert, Mike Quinn, for further insight. He offered a few more caterpillars of Texas butterflies that feed on plants of the genus Rhamnus, but not specifically on Rhamnus caroliniana (=Frangula caroliniana):

Spilosoma vestalis (Family Arctiidae)

Itame guenearia (Family Geometridae)

Pero macdunnoughi (Family Geometridae)

Triphosa californiata (Family Geometridae)

Cnidocampa flavescens (Family Limacodidae)

Celastrina argiolus (Family Lycaenidae)

And, as Mike says: "Arctiids are hairy, geometrids are inchworms, limacodids are generally
bizarre, and lycaenids are slug-like. None in my opinion are particularly bird-dropping like."

Mike pointed out that the classic bird-dropping larvae are those of the swallowtails. The only swallowtail reported to host on plants of the genus Rhamnus is the pale swallowtail (Papilio eurymedon) and it doesn't occur in Texas.

Nick Grishin, a professor at Southwestern Medical Center, suggested your larvae could possibly be sawfly larvae and not butterflies or moths at all. Sawflies are a group of insects in the order Hymenoptera, the same order that contains bees and wasps. Sawfly larvae do resemble butterfly and moth caterpillars and although there is no specific reference to any of them feeding on Carolina buckthorn or other species in the genus Rhamnus, they do feed on shrubs and trees and a few might be said to look a little like bird droppings.

So, these are some possibilities. If none of these looks like "your" larvae, perhaps you will see them again next year and can photograph them to send to Mr. SP for possible identification.