Solution 1:

I think if you said 'shingled beach' it would carry an implication that the shingle had been put there by humankind. But if you say 'shingle beach' it does not carry that message. In Britain we do not usually say 'pebbly beach' but sometimes you hear 'stony beach'.

Later edit

I am veering back to 'pebble-beach', having read others'comments. I think I was thrown off course by the word 'pebbly', which I do not recall hearing. It is interesting that the Brighton tourist office describes their beach as a 'pebble-beach'.

http://www.visitbrighton.com/things-to-do/beach-life

Solution 2:

The Oxford English Dictionary defines "shingled" as "Covered or tiled with shingles; Overlapping like tiles or shingles; (Of hair) cut in a shingle; (of a person) having the hair so cut". To describe a beach covered in shingle you'd be safe saying "a shingle beach".

Solution 3:

Shingle beach :

is a beach which is armoured with pebbles or small- to medium-sized cobbles (as opposed to fine sand). Typically, the stone composition may grade from characteristic sizes ranging from two to 200 mm.

Ngram shows that 'pebbly beach' is more common in AmE while Ngram 'shingle beach ' is more common in BrE.

Shingled beach is not a common definition and it suggests the idea of a beach that has been shingled for some specific purpose rather than a natural one.

Source:http://en.m.wikipedia.org/wiki/Shingle_beach