Information a little too late. Beech doesn't usually take conventional stains well. It tends to come out blotchy. I'm in the process of refinishing the same stock for the second time. The first time it came out nice but I didn't like the color.
I used then and will use again Minwax Polyshades aerosol. Just in a different color. It's basically a tinted Polyurethane clear coat. It says it's for indoors but I didn't have any trouble with it under normal shooting conditions. It's good because the color can be built up uniformly until you get the density you like. It also works great for laminate stocks which also don't take regular stains well.
Sorry I didn't see this earlier.
Hw30- .177- Vortek PG2, Tech sights
Hw30 Laminate- .177- Vortek PG2, Hawke
Airmax 2-7x32 AO.
Hw30-.177 Vortek PG3 steel, Hawke Vantage IR 2-7x32 AO
Hw50- .177- Vortek PG3, Hawke 4X non A/O
Hw95- .177- Vortek PG2, Hawke Airmax 3-9x40
Hw97SE (Green 77 Laminate stock)-.177 Vortek PG3, Hawke 4-12x40 Airmax
P1- 0.20 now .177
R1- 0.20 - Vortek Pg4, Hawke Airmax 3-9x40 AO
R9 SE (Blue Laminate stock) - 0.020- Vortek PG4, Hawke Airmax 3-9x40 AO